m+j+n {; Sylvie Gallet [101324,3444], 1997 ; Modified for IF..ELSE logic by Sylvie Gallet, March 1997 p0 = p3 - 1, iter = wait = 0 z = cm = pixel * exp(-flip(imag(p1)) * 0.01745329252) / abs(real(p1)) odev = continue = 1 : IF (iter < 300) IF (wait == 0) z = z*z + cm, odev = odev == wait wait = |z| >= 16 ENDIF ELSEIF (iter == 300) IF (wait == 0) odev = 1 ENDIF z = pixel ELSE IF (odev) zp0 = z^p0, d = zp0 * p3, n = zp0 * z - 1 z = -n/d + z, continue = |n| > 0.000001 ELSE z = z*z + p2, continue = |z| < 16 ENDIF ENDIF iter = iter + 1 continue ;SOURCE: ifs196.frm } m+j+n_2 {; Sylvie Gallet [101324,3444], 1997 ; Modified for IF..ELSE logic by Sylvie Gallet, March 1997 p0 = p3 - 1, odev = iter = wait = 0 z = cm = pixel * exp(-flip(imag(p1)) * 0.01745329252) / abs(real(p1)) continue = 1 : IF (iter < 300) IF (wait == 0) z = z*z + cm, odev = odev == wait wait = |z| >= 16 ENDIF ELSEIF (iter == 300) IF (wait == 0) odev = 0 ENDIF z = pixel ELSE IF (odev) zp0 = z^p0, d = zp0 * p3, n = zp0 * z - 1 z = -n/d + z, continue = |n| > 0.000001 ELSE z = z*z + p2, continue = |z| < 16 ENDIF ENDIF iter = iter + 1 continue ;SOURCE: ifs196.frm } m+j+n_2+if {; Sylvie Gallet [101324,3444], 1996 p0 = p3 - 1, odd = iter = wait = 0 z = cm = pixel * exp(-flip(imag(p1)) * 0.01745329252) / abs(real(p1)) : odd = odd == wait IF (iter < 300) IF (wait == 0) z = z*z + cm ENDIF bailout = |z| <= 16 IF (bailout == 0) z = 0, wait = 1, bailout = 1 ENDIF ELSE IF (iter == 300) IF (wait == 0) odd = 0, wait = 1 ENDIF z = pixel, bailout = 1 ELSE IF (odd) zp0 = z^p0, d = zp0 * p3, n = zp0 * z - 1 z = (-n/d+z), bailout = |n| > 0.000001 ELSE z = z*z+p2, bailout = |z| < 16 ENDIF ENDIF ENDIF iter = iter + 1 bailout ;SOURCE: 97msg.frm } m+j+n_3 {; Sylvie Gallet [101324,3444], 1996 ; real(p1) = size of the Mandelbrot set ; imag(p1) = rotation angle (degrees): negative = clockwise ; p2 = parameter for the Julia set ; p3 = exponent for the Newton set limit = trunc(maxit/2)*(maxit<600) + 300*(maxit>=600) p0 = p3 - 1 , odev = iter = tj = tn = tw = 0 , tm = 1 z = cm = pixel * exp(-flip(imag(p1)) * 0.01745329252) / abs(real(p1)): tw = tw || (|z| >= 16) || (iter == limit) z = (z*z+cm) * (tw == 0) + z * tw z = z * (iter != limit) + pixel * (iter == limit) zp0 = z^p0 , d = zp0 * p3 , n = zp0 * z - 1 z = (-n/d+z) * tn + z * tm + (z*z+p2) * tj iter = iter + 1 , odev = (odev == tw) tj = (odev == 0) && (iter > limit) tn = odev && (iter > limit) tm = (iter <= limit) tm || ((|z| < 16) && tj) || ((|n| > 0.000001) && tn) ;SOURCE: test.frm } M-J-rotation {; Jim Muth ; p1=power of Z, p2=rotation point, p3=rotation angle z=pixel, c=p2+(p3*pixel): z=z^p1-(1.1*z)+c |z| <=25 ;SOURCE: 97msg.frm } M-O-rotation {; Jim Muth ; real(p1)=power of Z, imag(p1)=angle of rotation ; p2=parallel planes, p3=rotation point and parallel planes a=real(p1), b=imag(p1)+.0000000000001 z=sin(b*.01745329251994)*real(pixel)+p2 c=cos(b*.01745329251994)*real(pixel)+flip(imag(pixel))+p3: z=z^a-(1.1*z)+c |z| <=25 ;SOURCE: 97msg.frm } M-P-rotation {; Jim Muth ; real(p1)=power of Z, imag(p1)=angle of rotation ; p2=parallel planes, p3=rotation point and parallel planes a=real(p1), b=imag(p1)+.0000000000001 z=sin(b*.01745329251994)*imag(pixel)+p2 c=cos(b*.01745329251994)*flip(imag(pixel))+real(pixel)+p3: z=z^a-(1.1*z)+c |z| <=25 ;SOURCE: 97msg.frm } M-R-rotation {; Jim Muth ; real(p1)=power of Z, imag(p1)=angle of rotation ; p2 and p3=rotation point and parallel planes a=real(p1), b=imag(p1)+.0000000000001 z=sin(b*.01745329251994)*flip(real(pixel))+p2 c=cos(b*.01745329251994)*real(pixel)+flip(imag(pixel))+p3: z=z^a-(1.1*z)+c |z| <=25 ;SOURCE: 97msg.frm } M-SetInNewton(XAXIS) {; use float=yes ; jon horner 100112,1700, 12 feb 93 z = 0, c = pixel, cminusone = c-1: oldz = z, nm = 3*c-2*z*cminusone, dn = 3*(3*z*z+cminusone) z = nm/dn+2*z/3 |(z-oldz)|>=|0.01| ;SOURCE: fractint.frm } m1 { z=0, c=pixel: z=sqr(z)+c c=c+p1 |z| <= 4 ;SOURCE: explode.frm } M3_Maxi (XYAXIS) {; A Mix on the basis of z^3+c. z = a = pixel IF(p1==0) bailout=8 ELSE bailout = |p1| ENDIF b = (-.5,.8660125403784) * pixel c = (-.5,-.8660125403784) * pixel: qz = sqr(z) * z u = qz + a v = qz + b w = qz + c au = |u| av = |v| aw = |w| IF(au>av) IF(au>aw) z = u ELSE z = w ENDIF ELSEIF(av>aw) z = v ELSE z = w ENDIF |z| <= bailout ;SOURCE: 97msg.frm } M3_Mini (XYAXIS) {; A Mix on the basis of z^3+c. ; May be quite slow on some machines! z = a = pixel IF(p1==0) bailout=8 ELSE bailout = |p1| ENDIF b = (-.5,.8660125403784) * pixel c = (-.5,-.8660125403784) * pixel: qz = sqr(z) * z u = qz + a v = qz + b w = qz + c au = |u| av = |v| aw = |w| IF(au<av) IF(au<aw) z = u ELSE z = w ENDIF ELSEIF(av<aw) z = v ELSE z = w ENDIF |z| <= bailout ;SOURCE: 97msg.frm } m4 { z=1-pixel^2: z=((fn1(flip(z)*z))+(fn2(sqr(z)*z)))+p1 |z|>=4 ;SOURCE: ad4.frm } m_juleye { z = pixel, c = (-0.7910322074096 , -0.1502158760371): z = z*z + c |z| < 4 ;SOURCE: 99msg.frm } M_Lagandre2 { c = P1, z = Pixel: z = (3 * z*z - 1) / 2 + c |z| < 100 ;SOURCE: fractint.frm } M_Lagandre3 { c = P1, z = Pixel: z = z * (5 * z*z - 3) / 2 + c |z| < 100 ;SOURCE: tchebych.frm } M_Lagandre4 { c = P1, z = Pixel: z = (z*z*(35 * z*z - 30) + 3) / 8 + c |z| < 100 ;SOURCE: tchebych.frm } M_Lagandre5 { c = P1, z = Pixel: z = z* (z*z*(63 * z*z - 70) + 15 ) / 8 + c |z| < 100 ;SOURCE: tchebych.frm } M_Lagandre6 { c = P1, z = Pixel: z = (z*z*(z*z*(231 * z*z - 315) + 105 ) - 5) / 16 + c |z| < 100 ;SOURCE: fractint.frm } M_Lagandre7 { c = P1, z = Pixel: z = z* (z*z*(z*z*(429 * z*z - 693) + 315) - 35 ) / 16 + c |z| < 100 ;SOURCE: tchebych.frm } M_Laguenew2 (XAXIS) { z = p1, c = pixel : z = (z*(z - 4) +2 ) / 2 + c |z| <=p2 ;SOURCE: newtchb2.frm } M_Laguenew3 (XAXIS) { z = p1, c = pixel : z = (z*(z*(-z + 9) -18) + 6 ) / 6 + c |z| <=100 ;SOURCE: newtchb2.frm } M_Laguenew4 (XAXIS) {; float=yes z = p1, c = pixel : z = (z * ( z * ( z * ( z - 16)+ 72) - 96)+ 24 ) / 24 + c |z| <=100 ;SOURCE: newtchb2.frm } M_Laguenew5(XAXIS) {; float=yes z = p1, c = pixel : z=(z*(z*(z*(z*(-z+25)-200)+600)-600)+120) / 120 + c |z| <=100 ;SOURCE: newtchb2.frm } M_Laguenew6 (XAXIS) {; float=yes z = p1, c = pixel : z=(z*(z*(z*(z*(z*(z-36)+450)-2400)+5400)-4320)+720) / 720 + c |z| <=100 ;SOURCE: newtchb2.frm } M_Laguerre2 { c = P1, z = Pixel: z = (z*(z - 4) +2 ) / 2 + c |z| < 100 ;SOURCE: tchebych.frm } M_Laguerre3 { c = P1, z = Pixel: z = (z*(z*(-z + 9) -18) + 6 ) / 6 + c |z| < 100 ;SOURCE: tchebych.frm } M_Laguerre4 { c = P1, z = Pixel: z = (z * ( z * ( z * ( z - 16)+ 72) - 96)+ 24 ) / 24 + c |z| < 100 ;SOURCE: tchebych.frm } M_Laguerre5 { c = P1, z = Pixel: z=(z*(z*(z*(z*(-z+25)-200)+600)-600)+120)/120+c |z| < 100 ;SOURCE: tchebych.frm } M_Laguerre6 { c = P1, z = Pixel: z=(z*(z*(z*(z*(z*(z-36)+450)-2400)+5400)-4320)+720)/ 720 + c |z| < 100 ;SOURCE: tchebych.frm } M_Legendre2 (XAXIS) { z = p1, c = pixel : z = (3 * z*z - 1) / 2 + c |z| <=100 ;SOURCE: newtcheb.frm } M_Legendre3 (XAXIS) { z = p1, c = pixel : z = z * (5 * z*z - 3) / 2 + c |z| <=100 ;SOURCE: newtcheb.frm } M_Legendre4 (XAXIS) { z = p1, c = pixel : z = (z*z*(35 * z*z - 30) + 3) / 8 + c |z| <=100 ;SOURCE: newtcheb.frm } M_Legendre5 (XAXIS) { z = p1, c = pixel : z = z* (z*z*(63 * z*z - 70) + 15 ) / 8 + c |z| <=100 ;SOURCE: newtcheb.frm } M_Legendre6 (XAXIS) {; float=yes z = p1, c = pixel : z = (z*z*(z*z*(231 * z*z - 315) + 105 ) - 5) / 16 + c |z| <=100 ;SOURCE: newtcheb.frm } M_Legendre7 (XAXIS) {; float=yes z = p1, c = pixel : z = z* (z*z*(z*z*(429 * z*z - 693) + 315) - 35 ) / 16 + c |z| <=100 ;SOURCE: newtcheb.frm } M_TchebychevC2 { c = P1, z = Pixel: z = c*(z*z-2) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevC3 { c = P1, z = Pixel: z = c*z*(z*z-3) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevC4 { c = P1, z = Pixel: z = c*(z*z*(z*z-4)+2) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevC5 { c = P1, z = Pixel: z = c*z*(z*z*(z*z-5)+5) |z|<100 ;SOURCE: fractint.frm } M_TchebychevC6 { c = P1, z = Pixel: z = c*(z*z*(z*z*(z*z-6)+9)-2) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevC7 { c = P1, z = Pixel: z = c*z*(z*z*(z*z*(z*z-7)+14)-7) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevS2 { c = P1, z = Pixel: z = c*(z*z-1) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevS3 { c = P1, z = Pixel: z = c*z*(z*z-2) |z|<100 ;SOURCE: fractint.frm } M_TchebychevS4 { c = P1, z = Pixel: z = c*(z*z*(z*z-3)+1) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevS5 { c = P1, z = Pixel: z = c*z*(z*z*(z*z-4)+3) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevS6 { c = P1, z = Pixel: z = c*(z*z*(z*z*(z*z-5)+6)-1) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevS7 { c = P1, z = Pixel: z = c*z*(z*z*(z*z*(z*z-6)+10)-4) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevT2 { c = P1, z = Pixel: z = c*(2*z*z-1) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevT3 { c = P1, z = Pixel: z = c*z*(4*z*z-3) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevT4 { c = P1, z = Pixel: z = c*(z*z*(8*z*z+8)+1) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevT5 { c = P1, z = Pixel: z = c*(z*(z*z*(16*z*z-20)+5)) |z|<100 ;SOURCE: fractint.frm } M_TchebychevT6 { c = P1, z = Pixel: z = c*(z*z*(z*z*(32*z*z-48)+18)-1) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevT7 { c = P1, z = Pixel: z = c*z*(z*z*(z*z*(64*z*z-112)+56)-7) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevU2 { c = P1, z = Pixel: z = c*(4*z*z-1) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevU3 { c = P1, z = Pixel: z = c*z*(8*z*z-4) |z|<100 ;SOURCE: fractint.frm } M_TchebychevU4 { c = P1, z = Pixel: z = c*(z*z*(16*z*z-12)+1) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevU5 { c = P1, z = Pixel: z = c*z*(z*z*(32*z*z-32)+6) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevU6 { c = P1, z = Pixel: z = c*(z*z*(z*z*(64*z*z-80)+24)-1) |z|<100 ;SOURCE: tchebych.frm } M_TchebychevU7 { c = P1, z = Pixel: z = c*z*(z*z*(z*z*(128*z*z-192)+80)-8) |z|<100 ;SOURCE: tchebych.frm } M_TchebycnewC2 (XAXIS) { z = p1, c = pixel : z = c*(z*z-2) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewC3 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(z*z-3) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewC4 (XAXIS) { z = p1, c = pixel : z = c*(z*z*(z*z-4)+2) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewC5 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(z*z*(z*z-5)+5) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewC6 (XAXIS) { z = p1, c = pixel : z = c*(z*z*(z*z*(z*z-6)+9)-2) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewC7 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(z*z*(z*z*(z*z-7)+14)-7) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewS2 (XAXIS) { z = p1, c = pixel : z = c*(z*z-1) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewS3 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(z*z-2) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewS4 (XAXIS) { z = p1, c = pixel : z = c*(z*z*(z*z-3)+1) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewS5 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(z*z*(z*z-4)+3) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewS6 (XAXIS) { z = p1, c = pixel : z = c*(z*z*(z*z*(z*z-5)+6)-1) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewS7 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(z*z*(z*z*(z*z-6)+10)-4) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewT2 (XAXIS) { z = p1, c = pixel : z = c*(2*z*z-1) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewT3 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(4*z*z-3) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewT4 (XAXIS) { z = p1, c = pixel : z = c*(z*z*(8*z*z+8)+1) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewT5 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*(z*(z*z*(16*z*z-20)+5)) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewT6 (XAXIS) { z = p1, c = pixel : z = c*(z*z*(z*z*(32*z*z-48)+18)-1) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewT7 (XAXIS) {; p1 must not = 0 z = p1, c = pixel: z = c*z*(z*z*(z*z*(64*z*z-112)+56)-7) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewU2 (XAXIS) { z =p1, c = pixel: z = c*(4*z*z-1) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewU3 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(8*z*z-4) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewU4 (XAXIS) { z = p1, c = pixel : z = c*(z*z*(16*z*z-12)+1) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewU5 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(z*z*(32*z*z-32)+6) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewU6 (XAXIS) { z = p1, c = pixel : z = c*(z*z*(z*z*(64*z*z-80)+24)-1) |z|<=100 ;SOURCE: newtchb2.frm } M_TchebycnewU7 (XAXIS) {; p1 must not = 0 z = p1, c = pixel : z = c*z*(z*z*(z*z*(128*z*z-192)+80)-8) |z|<=100 ;SOURCE: newtchb2.frm } maelstrom {; Giuseppe Zito z = pixel c1 = -0.524192 c7 = -0.430757 d0 = 0.222002 d4 = 0.893133 : x = real(z), y = imag(z) s0 = y s1 =c1 s0 = s0 *s1 s0 = s0 -x s0 = s0 -c7 newx = s0 s0 =d0 s0 = s0 -x s0 = s0 -d4 s0 = s0 *y s0 = s0 +x newy = s0 z = newx + flip(newy) newx < 4 && newx > -4 && newy < 4 && newy > -4 ;SOURCE: zg.frm } Mag1_J2 {; Copyright (c) Paul W. Carlson, 1998 ; p1 = Julia set coordinates ; real(p2) = controls size of elements ; imag(p2) not used ; real(p3) = number of color ranges ; imag(p3) = number of colors in a range ; z = iter = range_num = bailout = 0 pw = pixel c = p1 max_ratio = real(p2) num_ranges = real(p3) colors_in_range = imag(p3) factor = (colors_in_range - 1) / max_ratio : w = ((pw * pw + c - 1) / (pw + pw + c - 2))^2 ; ratio = |pw| / |w| pw = w IF (ratio < max_ratio && iter > 0) bailout = 1 z = factor * ratio + range_num * colors_in_range + 1 ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 && |w| < 1.0e20 ;SOURCE: 98msg.frm } magnet1j {; Chuck Ebbert. added 12 Jan 1993 ; p1 = Parameter c ; real(p2) = bailout (default is 100) z = pixel, cm1 = p1 - 1, cm2 = cm1 - 1 t = (100 * (real(p2)<=0) + real(p2) * (0<p2) ): z = sqr( (z*z+cm1 ) / (z+z+cm2 ) ) |z-1| > .000030517578 && |z| <= t ;SOURCE: builtn2.frm } magnet1j_2 { z = pixel, c1 = p1-1, c2 = p1-2, bailout = real(p2)*real(p2) : oldz = z z = (z*z + c1) / (z+z + c2) z = z*z |z-oldz| >= bailout ;SOURCE: 96msg.frm } magnet1m {; Chuck Ebbert. ; P1 = initial perturbation of z(0). ; real(p2) = bailout (default is 100) z = p1, cm1 = pixel - 1, cm2 = cm1 - 1 t = (100 * (real(p2)<=0) + real(p2) * (0<p2) ): z = sqr( (z*z+cm1 ) / (z+z+cm2 ) ) |z-1| > .000030517578 && |z| <= t ;SOURCE: builtn.frm } magnet2j {; Chuck Ebbert. added 12 Jan 1993 ; p1 = Parameter c ; real(p2) = bailout (default 100) z=pixel, c1=p1-1, c1x3=c1*3, c2x3=c1x3-3, c1c2=c1*c1-c1, c1c2p1=c1c2+1 t = (100 * (real(p2)<=0) + real(p2) * (0<p2) ): z = sqr( ( (z*z+c1x3 )*z+c1c2 ) / ( (z*3+c2x3 )*z+c1c2p1 ) ) |z-1| > .000030517578 && |z| <= t ;SOURCE: builtn2.frm } magnet2m {; Chuck Ebbert. ; P1 = initial perturbation of z(0). ; real(p2) = bailout (default 100) z=p1, c1=pixel-1, c1x3=c1*3, c2x3=c1x3-3, c1c2=c1*c1-c1, c1c2p1=c1c2+1 t = (100 * (real(p2)<=0) + real(p2) * (0<p2) ): z = sqr( ( (z*z+c1x3 )*z+c1c2 ) / ( (z*3+c2x3 )*z+c1c2p1 ) ) |z-1| > .000030517578 && |z| <= t ;SOURCE: builtn.frm } Magnetik { z = pixel + p1: z = (z-1)*(z+0.5)*(z*z+1) z = (z*0.3) - ((z)/fn1(z)) |z| < 4 ;SOURCE: magnetik.frm } Magnetik_2 { z = pixel + p1: z = (z-1)*((z*z) + z + 1.25) z = (z*0.3) - ((z)/fn1(z)) |z| < 4 ;SOURCE: magnetik.frm } Magnetik_3 { z = pixel + p1: z = (z-1)*((z*z) + z + 0.05) z = (z*0.3) - ((z)/fn1(z)) |z| < 4 ;SOURCE: magnetik.frm } Magnetik_4 { z = pixel + p1: z = (z*z*z) - 1 z = (z*0.3) - ((z)/fn1(z)) |z| < 4 ;SOURCE: magnetik.frm } Magnetik_5 { z = pixel: a = (z-1)*((z*z) + z + 1.25) b = (z-1)*(z+0.5)*((z*z)+1) z = z + ((a*z)/(a*z+(0.25*(-1))+(1-p1)*(b*z)/((b*z)-(0.5)*(-1)))) |z| < 4 ;SOURCE: magnetik.frm } man-jul-BJ6a {; Modified Sylvie Gallet [101324,3444], 1995 ; requires "periodicity=0" (<g> command) z = pixel, c = z, z2 = z*z, z3 = z*z2 compt=0, limit = real(p1), bailout = 4 p = (-0.743380900000982,-0.131850030300002) : test = (compt<limit) num = (z3 + p2*z2 + 1)^.5 denom = (1.5*z2 + p2*z)/num c = c*test+p*(1-test) z = fn1(z) - (num/denom) z2 = z*z z3 = z*z2 z = z*z+c compt = compt+1 p3 <= |z3 + p2*z2 + 1| ;SOURCE: sg-bc-bj.frm } man-newt-man {; Sylvie Gallet [101324,3444], 1995 +R.B. ; tiny mod on original Mandel-Newton by Sylvie ; tweaked brainlessly by Robin Bussell ; to give a hybrid mandel-newton fractal z = pixel, c = z, iter = 1, test1 = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center+rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (1-test1), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4) z = (z2+c)*test1 + (z-z1)*(1-test1) iter = iter+1 ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: forummsg.frm } man-newt-man2 {; Sylvie Gallet [101324,3444], 1995 +R.B. ; tiny mod on original Mandel-Newton by Sylvie ; tweaked brainlessly by Robin Bussell ; to give a hybrid mandel-newton fractal z = pixel, c = z, iter = 1, test1 = 1 ; rad = 3.1, center = (1.0,0.1) ; pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) ; zn = center+rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (1-test1) ; test2=(iter!=limit) ; z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4) z = (z2+c)*test1 + (z-z1)*(1-test1) iter = iter+1 ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: forummsg.frm } Man-XW-YW {; Jim Muth, Thanks to Benno ; p2 = 0 = Julibrot XW plane ; p2 = 1 = Julibrot YW plane ; p2 = >0 <1 = Oblique planes z=flip(real(pixel))+real(p1) c=flip(imag(pixel))+imag(p1) a=p2, b=flip(cos(asin(p2))): z=sqr(z)+((a+b)*c) |z| <= 25 ;SOURCE: 97msg.frm } Man-YZ-XZ {; Jim Muth ; p2 = 0 = Julibrot YZ plane ; p2 = 1 = Julibrot XZ plane ; p2 = >0 <1 = Oblique planes z=real(pixel)+flip(real(p1)) c=imag(pixel)+flip(imag(p1)) a=p2, b=flip(cos(asin(p2))): z=sqr(z)+((a+b)*c) |z| <= 25 ;SOURCE: 97msg.frm } man1-138 (XAxis) { z=c=pixel: z=(1-sqr(c))/sqr(1-c*fn1(z)) |z|<=4 ;SOURCE: 98msg.frm } man1-146 (XAxis) { z=c=pixel: z=sqr(fn1(z))/(1-c*fn2(z))^5 |z|<=4 ;SOURCE: 98msg.frm } man1-353ad (XAxis) { z=c=pixel: z=c*fn1(z)/fn2(z) |z|<=4 ;SOURCE: 98msg.frm } Man2-XW { z=flip(real(pixel))+real(p1) c=imag(pixel)+flip(imag(p1)): z=sqr(z)+c |z| <= 36 ;SOURCE: 97msg.frm } Man2-YW { z=real(p1)+flip(real(pixel)) c=imag(p1)+flip(imag(pixel)): z=sqr(z)+c |z| <= 36 ;SOURCE: 97msg.frm } Man2-YZ { z=real(pixel)+flip(real(p1)) c=flip(imag(pixel))+imag(p1): z=sqr(z)+c |z| <= 36 ;SOURCE: 97msg.frm } mand-BO-01 (XAXIS) {; from Absolutely_not - Paul Dickins - 1993 ; Classic M-set with bailout z <= p1 ; gives same results as BO-02 [ real(z)<=p1 ] z = (0,0), c = pixel : z = z * z + c z <= p1 ;SOURCE: bail_out.frm } mand-BO-02 (XAXIS) {; Jon Horner ; gives same results as BO-01 [ z <= p1 ] z = (0,0), c = pixel : z = z * z + c real(z) <= p1 ;SOURCE: bail_out.frm } mand-BO-03 {; Jon Horner ; asymmetric z = (0,0), c = pixel : z = z * z + c imag(z) <= p1 ;SOURCE: bail_out.frm } mand-BO-04 (XAXIS) {; Jon Horner ; integer and float give same image ; appears to be same as BO-08 [ abs(real(z)) <= p1 ] z = (0,0), c = pixel : z = z * z + c abs(z) <= p1 ;SOURCE: bail_out.frm } mand-BO-05 (XAXIS) {; from CAL - MandelbrotSet3 ; use float=yes z = (0,0), c = pixel : z = z * z + c |real(z) * imag(z)|<=|p1| ;SOURCE: bail_out.frm } mand-BO-06 (XAXIS) {; Jon Horner ; use float=yes z = (0,0), c = pixel : z = z * z + c |real(z)| <= p1 || |imag(z)| <= p1 ;SOURCE: bail_out.frm } mand-BO-07 {; Jon Horner ; asymmetric: use float=yes z = (0,0), c = pixel : z = z * z + c real(z) <= p1 || imag(z) <= p1 ;SOURCE: bail_out.frm } mand-BO-08 (XAXIS) {; from MandChimney - T.J.Hutton - Oct 1993 ; integer and float give same image ; appears to be same as BO-04 [ abs(z) <= p1 ] z = (0,0), c = pixel : z = z * z + c abs(real(z)) <= p1 ;SOURCE: bail_out.frm } mand-BO-09 (XAXIS) {; from MandTunnel - T.J.Hutton - Oct 1993 ; integer and float give same image z = (0,0), c = pixel : z = z * z + c abs(imag(z)) <= p1 ;SOURCE: bail_out.frm } mand-BO-10 {; from MandVariant - Warut Roonguthai ; Fractal Report 29, p9 - Oct 1993 ; simplified to `normal' conditions/loop by Jon Horner ; asymmetric z = (0,0), c = pixel : z = z * z + c real(z) + imag(z) <= p1 ;SOURCE: bail_out.frm } mand-BO-14 (XAXIS) {; Alan Wenham Feb 1993 ; applied to standard M-set formula by Jon Horner ; Using a transcendental function for bailout criteria z = (0,0), c = pixel : z = z * z + c abs(fn1(z)) <= 4 ;SOURCE: details.frm } mand_0 { z = c = sin(pixel): z = z*z + c |real(z)| <= 4 ;SOURCE: phctutor.frm } mand_1 { z = c = pixel: z = z*z + c |z| <= 4 ;SOURCE: phctutor.frm } mand_2 { z = c = 1/pixel: z = z*z + c |imag(z)| <= 4 ;SOURCE: phctutor.frm } mand_3 { z = c = -pixel: z = z*z + c |real(z)+imag(z)| <= 4 ;SOURCE: phctutor.frm } Mand_Atan_Mset {; Copyright (c) Paul W. Carlson, 1998 w = z = iter = range_num = bailout = 0 c = pixel num_ranges = real(p2) colors_in_range = imag(p2) : prev_w = w w = w * w + c IF (abs(real(w)) > p1) bailout = 1 angle = abs(atan((imag(w)-imag(prev_w))/(real(w)-real(prev_w)))) index = 2 * colors_in_range * angle / pi z = index + range_num * colors_in_range + 1 ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 ;SOURCE: 98msg.frm } Mand_Ellipse {; Copyright (c) Paul W. Carlson, 1998 ; real(p1) = ellipse real axis ; imag(p1) = ellipse imag axis ; real(p2) = number of color ranges ; imag(p2) = number of colors in a range ; z = w = k = iter = range_num = bailout = 0 c = pixel a = real(p1) b = imag(p1) num_ranges = real(p2) colors_in_range = imag(p2) colors_in_range_1 = colors_in_range - 1 : w = w * w + c ; dist = real(w) * real(w) / a + imag(w) * imag(w) / b IF (dist > 1) bailout = 1 index = colors_in_range_1 * (dist - 1) / dist z = index + range_num * colors_in_range + 1 ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 ;SOURCE: 98msg.frm } MandConj01 (XAXIS) {; Paul J. Horn, see MandelConj. ; This is a variation on a theme. z = c = Pixel: z = Sqr(z) + Conj(Pixel) |z| <= 4 ;SOURCE: pjhcon.frm } MandConj02 (XAXIS) {; Paul J. Horn, see MandelConj. ; Another variation on the theme. z = c = Pixel: z = Sqr(Conj(z)) + Conj(Pixel) |z| <= 4 ;SOURCE: pjhcon.frm } MandConj03 (XAXIS) {; Paul J. Horn ; yet another variation on the theme z = c = Pixel: z = Sqr(conj(z))*conj(z) + Pixel |z| <= 4 ;SOURCE: pjhcon.frm } MandConj04 (XAXIS) {; Paul J. Horn ; yet another variation on the theme z = c = Pixel: z = Sqr((z))*(z) + Conj(Pixel) |z| <= 4 ;SOURCE: pjhcon.frm } MandConj05 (XAXIS) {; Paul J. Horn ; yet another variation on the theme z = c = Pixel: z = Sqr(conj(z))*conj(z) + Conj(Pixel) |z| <= 4 ;SOURCE: pjhcon.frm } MandConj06 (XAXIS) {; Paul J. Horn ; yet another variation on the theme z = c = Pixel: z = Sqr(Sqr(conj(z))) + Pixel |z| <= 4 ;SOURCE: pjhcon.frm } MandConj07 (XAXIS) {; Paul J. Horn ; yet another variation on the theme z = c = Pixel: z = Sqr(Sqr((z))) + Conj(Pixel) |z| <= 4 ;SOURCE: pjhcon.frm } MandConj08 (XAXIS) {; Paul J. Horn ; yet another variation on the theme z = c = Pixel: z = Sqr(Sqr(conj(z))) + Conj(Pixel) |z| <= 4 ;SOURCE: pjhcon.frm } MandConj09 {; Paul J. Horn ; yet another variation on the theme z = c = Pixel: z = (conj(z))^p1 + Pixel |z| <= 4 ;SOURCE: pjhcon.frm } MandConj10 {; Paul J. Horn ; yet another variation on the theme z = c = Pixel: z = z^p1 + Conj(Pixel) |z| <= 4 ;SOURCE: pjhcon.frm } MandConj11 {; Paul J. Horn ; yet another variation on the theme z = c = Pixel: z = (conj(z))^p1 + Conj(Pixel) |z| <= 4 ;SOURCE: pjhcon.frm } mandel { ; p1=initial perturbation of z ; bailout is real(p2) (default 4) z = pixel + p1 t = (4 * (real(p2)<=0) + real(p2) * (0<p2) ): z = sqr(z) + pixel |z| <= t ;SOURCE: builtn.frm } Mandel+ls {; Normal formula: with "LHS" ; requires 'periodicity=0' x=real(scrnpix)/real(scrnmax) y=(imag(scrnmax)-imag(scrnpix))/imag(scrnmax) z=x+flip(y) chrL1 = x<0.868||y<0.028&&x>0.86&&x<0.884 chrH2 = x<0.896||x>0.912||(y<0.044&&y>0.036)&&x>0.888&&x<0.92 chrS3 = abs(cabs(z+(-0.936,-0.048))-0.008)<0.004&&(x<0.936||y>0.048) \ ||(abs(cabs(z+(-0.936,-0.032))-0.008)<0.004&&(x>0.936||y<0.032)) test = chrL1||chrH2||chrS3&&y>0.02&&y<0.06 z = c = pixel: z = z*z + c |z| <= 4&&test==0 ;SOURCE: 9609.frm } mandel-julia {; Sylvie Gallet 1995 z=pixel, c=z compt=0, limit=real(p1), bailout=4 p=(-0.743380900000982,-0.131850030300002) : test=(compt<limit) c=c*test+p*(1-test) z=z*z+c compt=compt+1 |z|<=bailout ;SOURCE: mandj.frm } mandel-lambdafn {; Sylvie Gallet [101324,3444], 1995 ; requires "periodicity=0" (<g> command) c = z = pixel, lambda = (1.0,0.4) pix2 = pixel*4+0.8, compt = 0, limit = real(p1) : test1 = (compt<limit), test2 = (compt!=limit) z = (z-pix2)*test2 + pix2 bailout = 4096 - 4032*test1 z2 = lambda*sin(z) z = (z*z+c-z2)*test1+z2 compt = compt+1 |z| <= bailout ;SOURCE: gallet-1.frm } mandel-lambdafn-3 {; Sylvie Gallet [101324,3444], 1995 ; requires "periodicity=0" c = z = pixel, lambda = (1.0,0.4), test0 = 1, test3=0 pix2 = pixel*4+0.8, iter= 0, limit = real(p1) : test1 = (iter<limit), test0 = 1-test0, test2 = (iter!=limit) z = (z-pix2)*test2 + pix2 bailout = 4096 - 4032*test1 z2 = lambda*sin(z) z = (z*z+c-z2)*test1+z2 test3 = (test3 || (|z|>bailout)) z = z*(1-(test3 && test0 && test1)) iter = iter+1 |z| <= bailout ;SOURCE: gallet-2.frm } mandel-lambdafn_2 {; Sylvie Gallet [101324,3444], 1995 ; requires "periodicity=0" (<g> command) c = z = pixel, lambda = (1.0,0.4) pix2 = pixel*4+0.8, compt = 0, limit = real(p1) : test1 = (compt<limit), test2 = (compt!=limit) z = (z-pix2)*test2 + pix2 bailout = 20000 + 1000*test1 ; the bug is here... z2 = lambda*sin(z) z = (z*z+c-z2)*test1+z2 compt = compt+1 |z| <= bailout ;SOURCE: gallet-1.frm } mandel-mandel {; Sylvie Gallet 1995 c1=(0.34396372130558980 , 0.05608272738673762) c2=(-0.72141758920523890 , 0.25918045895127010) c=z=pixel, delta=c2-c1, b=c+delta compt=0, limit=real(p1), bailout=16 : test1=(compt<limit), test2=(compt!=limit) z = z * test2 c = b - delta * test1 z=z*z+c compt=compt+1 |z|<=bailout ;SOURCE: mandelm.frm } mandel-newton {; Sylvie Gallet [101324,3444], 1995-1996 ; Formula designed for Fractint 19.2 and modified for Fractint 19.3 z = pixel, c = z, iter = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center+rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (iter<limit), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4+(z==0)) z = (z2+c)*test1 + (z-z1)*(1-test1) iter = iter+1 ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: gallet-n.frm } mandel-newton-2 {; Sylvie Gallet [101324,3444], 1995-1996 ; Formula designed for Fractint 19.2 and modified for Fractint 19.3 limit = real(p1), test0 = 1, test3=0, iter = 1 z = pixel, c = z, b1 = 16 rad = 6, pix = (10*pixel+(8.0,-5))*(-0.1,-0.95) center = (1.0,0.1), zn = center+rad/(pix-center), b2 = 0.0001 : test0 = 1-test0, test1 = (iter<limit), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4 + (z==0)) z = (z2+c)*test1 + (z-z1)*(1-test1) test3 = (test3 || (|z|>b1)) z = z*(1-(test3 && test0 && test1)) iter = iter+1 ((|z|<=b1)*test1) || ((|z1|>=b2)*(1-test1)) ;SOURCE: gallet-n.frm } mandel-newton_a {; Modified Sylvie Gallet frm [101324,3444], 1995 z = pixel, c = z, iter = 1 rad = 3.1, center = (-3.6,-3.0) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = fn1(center+rad)/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (iter<limit), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4) z = (z2+c)*test1 + (z-z1)*(1-test1) iter = iter+1 ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: bej3.frm } mandel-newton_j4 {; Modified Sylvie Gallet Frm [101324,3444], 1995 z = pixel, c = z, iter = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center+rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (iter<limit), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = fn1(fn2(z*z+c)), z4 = z2*z2, z1 = (z4*z-1)/(4*z4) z = (z2+fn3(c))*test1 + (z-z1)*(1-test1) iter = iter+(3.099,-3.099) ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: bej4.frm } mandel-newton_j5 {; Modified Sylvie Gallet Frm [101324,3444], 1995 z = pixel, c = z, iter = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center+rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (iter<limit), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = fn1((z*z)/(zn)), z4 = z2*z2, z1 = (z4*z-1)/(4*z4) z = (z2+(c))*test1 + (z-z1)*(1-test1) iter = iter+fn2(3.099,-3.099) ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: bej4.frm } mandel-newton_j6c {; Modified Sylvie Gallet Frm [101324,3444], 1995 z = pixel, c = z, iter = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center/rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (iter<limit), test2=(iter!=limit) c=(-0.7456,-0.0186) c=fn1(sin(conj(-0.81256,-0.1295))) z = (z-zn)*test2 + zn z2 = (z*z)-(zn), z4 = (z2*z2), z1 = (z4*z-1)/(4*z4) z = (z2+(c))*test1 + (z-z1)*(1-test1) iter = iter+(3.099,-3.099) ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: bej4.frm } mandel-newton_j6e {; Modified Sylvie Gallet Frm [101324,3444], 1995 z = pixel, c = z, iter = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center/rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (iter<limit), test2=(iter!=limit), test3=(zn^limit) c=(-0.7456,-0.0186) c=sin(conj(-0.81256,-0.1295)) z = (z-zn)*test2 + zn z2 = fn1(z*z/c)-(zn), z4 = (z2*z2), z1 = (z4*z-1)/(4*z4) z = (z2+(c))*test1 + (z-z1)*(1-test1) iter = iter+(2.079,-2.079) ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: bej4.frm } mandel-newton_j6g {; Modified Sylvie Gallet Frm [101324,3444], 1995 ; Revised for Fractint v20 by G. Martin z = pixel, c = z, iter = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center/rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (iter<limit), test2=(iter!=limit) c1=(-0.7056,-0.0086) c=fn1(fn2(conj(-0.80256,-0.1095))) z = (z-zn)*test2 + zn z2 = (z^2+(-0.6956,0.10)+(test1/7*pixel)), z4 = (z2*z2) z1 = (z4*z-1)/(4*z4) z = (z2+(c))*test1 + (z-z1)*(1-test1) iter = iter+(3.099,-3.099) ((|z2| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: bej4.frm } mandel-newton_j7c3 {; Sylvie Gallet [101324,3444], 1995 z = pixel, c = z, iter = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center*rad+(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (iter&&limit), test2=(iter!=limit) c1=(-0.7056,-0.0086) c=fn1(sin(conj(-0.80256,-0.1095))) z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4) z = fn2(z2)+(c*test1) + (z-z1)*(1-test1) iter = iter+1 ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: sg-bc-bj.frm } Mandel3 {; Fractal Creations example z = pixel, c = sin(z): z = (z*z) + c z = z * 1/c |z| <= 4 ;SOURCE: fractint.frm } mandel4 {; Chuck Ebbert added 12 Jan 1993 ; p1=initial perturbation of z ; bailout is real(p2) (default 4) z = pixel + p1, c = pixel t = (4 * (real(p2)<=0) + real(p2) * (0<p2) ): z = sqr(z*z) + c ; 13 Jan 1993 |z| <= t ;SOURCE: builtn2.frm } Mandel[Fn||Fn] {; v18 - Jonathan Osuch ; Note: use floating point ; Edited for Fractint v. 20 by George Martin, 10/98 z = p1, shift = real(p2), x=|z|: IF (x<shift) z=pixel+fn1(z) ELSE z=pixel+fn2(z) ENDIF x=|z| x<=64 ;SOURCE: parser.frm } Mandel_3Way {; Copyright (c) Paul W. Carlson, 1998 ; Alyways use float=y, outdide=summ ; real(p1) = escape circle radius squared ; imag(p1) = number of iterations to skip ; real(p2) number of color ranges ; imag(p2) number of colors in a range z = w = k = iter = range_num = bailout = 0 c = pixel prev_modw2 = 1.0e20 rad2 = real(p1) skip_iters = imag(p1) num_ranges = real(p2) colors_in_range = imag(p2) colors_in_range_1 = colors_in_range - 1 : w = w * w + c ; IF ((prev_modw2 < rad2) && (|w| > rad2)) bailout = 1 IF (iter > skip_iters) k = 1 ENDIF index = colors_in_range_1 * (rad2 - prev_modw2) / rad2 z = (index + range_num * colors_in_range + 1) * k ENDIF prev_modw2 = |w| range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 && |w| <= rad2 ;SOURCE: 98msg.frm } Mandel_4-D {; 4-D Mandelbrot, 8-D Julibrot a=(p1), b=(0,0), d=p2+2: f=sqr(a)-sqr(b)+pixel b=d*a*b+p3 a=f |a|+|b| <16 ;SOURCE: 98msg.frm } Mandel_4-Dd {; 4-D Mandelbrot, 8-D Julibrot a=(p1), b=(0,0), d=p2+2: f=sqr(a)-sqr(b)+pixel b=d*a*b+p3 a=f |a|/|b| <16 ;SOURCE: 98msg.frm } Mandel_4-Ddr {; 4-D Mandelbrot, 8-D Julibrot a=(p1), b=(0,0), d=p2+2: f=sqr(a)-sqr(b)+pixel b=d*a*b+p3 a=f |b|/|a| <16 ;SOURCE: 98msg.frm } Mandel_4-Dm {; 4-D Mandelbrot, 8-D Julibrot a=(p1), b=(0,0), d=p2+2: f=sqr(a)-sqr(b)+pixel b=d*a*b+p3 a=f |a|*|b| <16 ;SOURCE: 98msg.frm } Mandel_4-Ds {; 4-D Mandelbrot, 8-D Julibrot a=(p1), b=(0,0), d=p2+2: f=sqr(a)-sqr(b)+pixel b=d*a*b+p3 a=f |a|-|b| <16 ;SOURCE: 98msg.frm } Mandel_alt { ;(c) 1993 by: ; ; LRCMIKE@LRC.OLDSCOLLEGE.AB.CA ; ; Michael G. Wareman ; P.O. Box 1856 ; Olds, Alberta, Canada ; T0M 1P0 z = c = pixel: z = z * z + c |z - pixel| < 4 ;SOURCE: frame.frm } Mandel_alt_3 { ;(c) 1993 by: ; ; LRCMIKE@LRC.OLDSCOLLEGE.AB.CA ; ; Michael G. Wareman ; P.O. Box 1856 ; Olds, Alberta, Canada ; T0M 1P0 z = c = pixel: z = z * z + c |z + pixel| < 4 ;SOURCE: frame.frm } mandel_nest {; George Martin [76440,1143] with help from Sylvie Gallet ; periodicity=0 float=yes, fractint v19.3 or higher ; real(p1) is reduction factor, e.g 1 (default) is same size, ; 2 is half the size (linear; 1/4 the area size) ; imag(p1) is clockwise rotation of the image in degrees ; p2 - real portion moves image along the x axis, imag ; portion along the y axis. + = right,up. ; real(p3) - iteration spacing. 256 and multiples causes ; nested images to have same coloring. Default 256 z=0, c=pixel newpixel=pixel, iter=0 reduction=real(p1) + (real(p1)==0) nextzoom=iterspace=(p3>0)*p3 + (p3<=0)*256 rotation=pi*flip(imag(p1))/180: test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace newpixel=newpixel*(1-test)+test*reduction*(newpixel-p2)*exp(rotation) z = z*(1 - test) c = c*(1 - test) + test*newpixel z = z*z + c iter = iter + 1 |z| <= 16 ;SOURCE: nest.frm } Mandel_Other { ;(c) 1993 by: ; ; LRCMIKE@LRC.OLDSCOLLEGE.AB.CA ; ; Michael G. Wareman ; P.O. Box 1856 ; Olds, Alberta, Canada ; T0M 1P0 ; Edited by G. Martin, 5/8/98, to correct obvious typo (":" missing) z = c = pixel: z = z * z * z * z + c |z| < |c| ;SOURCE: frame.frm } MANDEL_RI (XAXIS) {; Zoom near the seahorse valley Z=C=PIXEL: Z=SQR(Z)+P1 Q=10*(|IMAG(Z)|<.0001) O=10*(|REAL(Z)|<.0001) P=(|Z|>=20)*10 O+P+Q<=9 ;SOURCE: ramiro.frm } Mandel_Rings {; Copyright (c) Paul W. Carlson, 1998 z = w = k = iter = range_num = bailout = 0 c = pixel ring_width = real(p1) num_ranges = real(p2) colors_in_range = imag(p2) index_factor = (colors_in_range - 1) / ring_width : w = w * w + c ; dist = abs(|w|-.25) IF (dist < ring_width && iter > 0) bailout = 1 z = index_factor * dist + range_num * colors_in_range + 1 ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 && |w| < 1.0e20 ;SOURCE: carlson2.frm } Mandel_Segs {; Copyright (c) Paul W. Carlson, 1998 ; real(p1) = stalk segment width factor ; imag(p1) = stalk segment length factor ; real(p2) = number of color ranges ; imag(p2) = number of colors in a range ; real(p3) = minimum |w| for stalks ; imag(p3) = minimum iterations ; c = pixel w = z = bailout = iter = range_num = 0 stalk_width = real(p1) num_ranges = real(p2) colors_in_range = imag(p2) min = real(p3) index_factor = (colors_in_range - 1) / stalk_width stalk_len = imag(p1) * stalk_width * stalk_width : w = w * w + c ; IF (abs(real(w)) <= abs(imag(w))) dist = abs(real(w)) ELSE dist = abs(imag(w)) ENDIF IF (dist < stalk_width && iter > imag(p3)) IF (|w| > min && |w| < stalk_len) z = index_factor * dist + range_num * colors_in_range + 1 bailout = 1 ENDIF ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 && |w| < 4 ;SOURCE: 98msg.frm } Mandel_Squares {; Copyright (c) Paul W. Carlson, 1998 ; Parameters: ; real(p1) = controls the size of the squares (0.1 to 0.8) ; imag(p1) = 0 if Mset, else Julia set ; p2 = Julia set coordinates ; real(p3) = number of iterations to skip ; IF (imag(p1) == 0) c = pixel w = 0 ELSE c = p2 w = pixel ENDIF z = bailout = iter = range_num = 0 shield_size = real(p1) skip_iters = real(p3) num_ranges = 8 colors_in_range = 30 k = 0.5 + shield_size j = 0.5 - shield_size index_factor = 29 / shield_size: ;**************************************************** w = w * w + c ;**************************************************** awr = abs(real(w)), awi = abs(imag(w)) IF ((awr < k) && (awr > j) && (awi < k) && (awi > j)) awr5 = abs(awr - 0.5), awi5 = abs(awi - 0.5) IF (awr5 <= awi5) min_dist = awr5 ELSE min_dist = awi5 ENDIF IF (min_dist < shield_size && iter > skip_iters) z = index_factor * min_dist + range_num * colors_in_range + 1 bailout = 1 ENDIF ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 && |w| < 1.0e20 ;SOURCE: 98msg.frm } Mandel_xt(XAXIS_NOIMAG) {; Variation with x und z variable ; real(p1) = imaginary part of u ; imag(p1) = real part of v u=real(pixel)+flip(real(p1)) z=v=imag(p1)+flip(imag(pixel)) bailout=5+2.5*(|u|+|v|): z=sqr(z)+u |z|<bailout ;SOURCE: 97msg.frm } Mandel_xz(XAXIS_NOIMAG) {; Variation with x und z variable ; real(p1) = imaginary part of u ; imag(p1) = imaginary part of v u=real(pixel)+flip(real(p1)) z=v=imag(pixel)+flip(imag(p1)) bailout=5+2.5*(|u|+|v|): z=sqr(z)+u |z|<bailout ;SOURCE: 97msg.frm } Mandel_yt(ORIGIN) {; Variation with x und z variable ; real(p1) = real part of u ; imag(p1) = real part of v u=real(p1)+flip(real(pixel)) z=v=imag(p1)+flip(imag(pixel)) bailout=5+2.5*(|u|+|v|): z=sqr(z)+u |z|<bailout ;SOURCE: 97msg.frm } Mandel_yz (ORIGIN) {; Variation with x und z variable ; real(p1) = real part of u ; imag(p1) = imaginary part of v u=real(p1)+flip(real(pixel)) z=v=imag(pixel)+flip(imag(p1)) bailout=5+2.5*(|u|+|v|): z=sqr(z)+u |z|<bailout ;SOURCE: 97msg.frm } MandelBar_3_c (xaxis) {; Jm Collard-Richard z=c=pixel: z=conj(z)^3+c |z|<=4 ;SOURCE: jmcr1.frm } MandelBar_4_c (xaxis) {; Jm Collard-Richard z=c=pixel: z=conj(z)^4+c |z|<=4 ;SOURCE: jmcr1.frm } MandelBar_N {; Jm Collard-Richard z=c=pixel: z=conj(z)^p1+c |z|<=4 ;SOURCE: jmcr1.frm } MandelBarFN (xaxis) {; Jm Collard-Richard z=c=pixel: z=c*fn1(conj(z)) |z|<=64 ;SOURCE: jmcr1.frm } Mandelbrot (XAXIS) {; Mark Peterson ; Classical fractal showing LastSqr speedup z = Pixel, z = Sqr(z): ; Start with z**2 to initialize LastSqr z = z + Pixel z = Sqr(z) LastSqr <= 4 ; Use LastSqr instead of recalculating ;SOURCE: fractint.frm } Mandelbrot2 { z = Pixel, x=abs(real(z)), y=abs(imag(z)) tx = (x>0.5) + (x>1) + (x>1.5) + (x>2) ty = (y>0.5) + (y>1) + (y>1.5) x = 0.5*(-tx*(real(z)<0) + (tx-1)*(real(z)>=0)) y = 0.5*(-ty*(imag(z)<0) + (ty-1)*(imag(z)>=0)) z = x + flip(y), z = Sqr(z): z = z + Pixel z = Sqr(z) LastSqr <= 4 ;SOURCE: 96msg.frm } Mandelbrot3 { z = Pixel, x=abs(real(z)), y=abs(imag(z)) tx = (x>0.5) + (x>1) + (x>1.5) + (x>2) ty = (y>0.5) + (y>1) + (y>1.5) x = 0.5*tx*real(z)/x, y = 0.5*ty*imag(z)/y z = x + flip(y), z = Sqr(z): z = z + Pixel z = Sqr(z) LastSqr <= 4 ;SOURCE: 96msg.frm } Mandelbrot_JM {; Jim Muth z=p1, c=pixel: z=sqr(z)+c |z| <=p2 ;SOURCE: 0from_ml.frm } Mandelbrot_JM2 {; Jim Muth z=p1, c=pixel+p2: z=sqr(z)+c |z| <= 16 ;SOURCE: 0from_ml.frm } MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c |z| <= 16 ;SOURCE: 99msg.frm } MandelbrotInNewton(XAXIS) {; use float=yes: from CAL v4.0 by Tim Harris z = 0, c = pixel, cminusone = c-1: oldz = z nm = 3 * c-2 * z * cminusone dn = 3 * (3 * z * z + cminusone) z = nm/dn + 2 * z/3 |(z-oldz)|>=|0.01| ;SOURCE: mnewton.frm } MandelbrotJM {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=sqr(z)+c |z| <= 16 ;SOURCE: 98msg.frm } MandelbrotMiN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=(-z)^(b)+c |z| <= 16 ;SOURCE: 98msg.frm } MandelbrotMix {; Jim Muth z=p3, c=pixel a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=(a*(z^b))+(d*(z^f))+c |z| <= 100 ;SOURCE: 97msg.frm } MandelbrotMix1 {; Jay Hill mod of Jim Muth eqn. ; both d and f must be non-zero, and b not equal f c=pixel, a=real(p1), b=imag(p1), d=real(p2), f=imag(p2) z=(-a*b/f/d)^(1/(f-b)): ; critical point z=(a*(z^b))+(d*(z^f))+c |z| <= 100 ;SOURCE: 98msg.frm } MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1 l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c |z| < l ;SOURCE: 99msg.frm } MandelbrotMix4_v1 {; Jim Muth c=pixel, a=real(p1), b=imag(p1), d=real(p2), f=imag(p2) g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j: z=(a*(z^b))+(d*(z^f))+c |z| <= 100 ;SOURCE: 98msg.frm } MandelbrotMix4a {; Jim Muth ; "a" suffix added by L.StClair 3/6/99 ; to differentiate this version from the one previously posted a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1 l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c |z| < l ;SOURCE: frac_ml.frm } MandelbrotMix5 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1 l=imag(p3)+1, c=pixel: z=k*((a*(z^b))+(d*(z^f)))+c^l |z| < 100 ;SOURCE: 98msg.frm } MandelbrotMix5_v1 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, c=pixel/(a*d): z=(a*(z^b))+(d*(z^f))+c |z| <= 100 ;SOURCE: 98msg.frm } MandelbrotMix6 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1 l=imag(p3)+100, c=pixel*k: z=(a*(z^b))+(d*(z^f))+c |z| <= l ;SOURCE: 98msg.frm } MandelbrotMix7 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1 l=imag(p3)+100, c=pixel: z=k*((a*(z^b))+(d*(z^f)))+c |z| <= l ;SOURCE: 98msg.frm } MandelbrotMix7_v1 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1 l=imag(p3)+100, c=pixel*k: z=(a*((-z)^b))+(d*((-z)^f))+c |z| <= l ;SOURCE: 98msg.frm } MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c |z| <= 16 ;SOURCE: 98msg.frm } MandelbrotPanorama {; Jay Hill, 1998 ; Panorama Mandelbrot set z = 0, c = exp(flip(pixel))+p2: z = z*z + c |z| < 4 ;SOURCE: 98msg.frm } MandelbrotPM {; formula Jim Muth z=p1+10^(-100), c=pixel: z=p2*(.5*((-z)^p3+z^p3))+c |z| <= 250 ;SOURCE: 98msg.frm } MandelbrotQud {; Jim Muth z=p3, c=pixel a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=sqr(z)+(.2*(z*z*z))+(a*(z^b))+(d*(z^f))+c |z| <= 100 ;SOURCE: 98msg.frm } MandelbrotTri {; Jim Muth z=p3, c=pixel a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=(z*z*z)+(a*(z^b))+(d*(z^f))+c |z| <= 100 ;SOURCE: 98msg.frm } MandelbrotVB {; Jim Muth z=p1, c=pixel+p3 a=sqr(p2): z=sqr(z)+c |z| <= a ;SOURCE: 97msg.frm } MandelbrotVB_new {; Jim Muth z=p1, c=pixel+p3 a=sqr(p2): z=sqr(z)+c |z| <= a ;SOURCE: frac_art.frm } MandelbrotZC {; Jim Muth z=p3, c=pixel: z=(real(p1)*(z^imag(p1)+c))+(real(p2)*(c^imag(p2)+z)) |z| <= 100 ;SOURCE: 97msg.frm } MandelbrotZC-rev {; Jim Muth z=p3, c=pixel: z=(real(p1)*(z^imag(p1)+c))+(real(p2)*(c^imag(p2)+z)) |z| <= 100 ;SOURCE: 0from_ml.frm } MandelbrotZC2 {; Jim Muth z=p1, c=pixel: z=real(p2)*(z^imag(p2)+c)+real(p3)*(c^imag(p3)+z) |z| <= 100 ;SOURCE: frac_art.frm } MandelConj (XAXIS) {; Paul J. Horn, this was mentioned in Pickover's book ; Computers, Chaos, Patterns and Beauty. ; He didn't give the forumula, so I came up with this z = c = Pixel: z = Sqr(conj(z)) + Pixel |z| <= 4 ;SOURCE: pjhcon.frm } MandelCosine (XYAXIS) { z = pixel: z = cos(z) * pixel |z| <= 50 ;SOURCE: fracv13r.frm } Mandelcubic (XYAXIS) {; Dewey Odhner z = Pixel, z = Sqr(z)*z: ; Start with z**3 to initialize LastSqr z = z + Pixel z = Sqr(z)*z LastSqr <= 4 ; Use LastSqr instead of recalculating ;SOURCE: dragbat.frm } MandelFn(XYAXIS) {; Jon Horner [ not the same as hard-coded type !! ] z = c = pixel : z = fn1(z) * c |z| <= 64 ;SOURCE: parser.frm } Mandelfn1 {; make fn1=recip and inside=zmag ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=0, z=0: ee=sqr(ee)+pixel z=fn1(ee) |ee|<=4 ;SOURCE: ramiro.frm } MandelFnA (XYAXIS) {; from LambdaFn - Chuck Ebbert - from BUILTN.FRM ; this one ain't right either! ; p1 is lambda, real(p2) changes bailout (default = 64). z = m, c = pixel: m = ((1.0,0.0) * (|p1|<=0) + p1 ) t = (64 * (real(p2)<=0) + real(p2) * (0<p2) ) z = fn1(z) * c abs(imag(z)) <= t && abs(real(z)) <= t ;SOURCE: parser.frm } Mandelglass (XAXIS) { z = (0.5, 0.0): z = pixel * z * (1 - z) |z| <= 4 ;SOURCE: fracv13r.frm } MandelHypCosine (XYAXIS) { z = pixel: z = cosh(z) * pixel |z| <= 50 ;SOURCE: fracv13r.frm } MandelHypSine (XYAXIS) { z = pixel: z = sinh(z) * pixel |z| <= 50 ;SOURCE: fracv13r.frm } MandelIke {; Ron Barnett [70153,1233], 1996 Requires passes=1 ; p3 will shift the ikenaga set wrt the mandelbrot set ; Ron Barnett, 1996 z = pixel+(whitesq==0)*p3 c = whitesq*p1*pixel + (whitesq==0)*p2*pixel: z=whitesq*(z*z*z+(c-1)*z-c) + (whitesq==0)*(z*z+c) |z|<=4 ;SOURCE: phc.frm } Mandelion { z = c = 1/pixel: z = sin(sqr(c)) * sin(-z) |z| <= 64 ;SOURCE: 98msg.frm } Mandelion1 { z = c = 1/pixel: z = sin(sqr(c*z)) * sin(-z) |z| <= 64 ;SOURCE: 98msg.frm } Mandelion2 { z = c = 1/pixel: z = sin(sqr(c)*z) * sin(-z) |z| <= 64 ;SOURCE: 98msg.frm } MandelJulia (XAXIS) {; Pretty sick. Try your every fave julias for p1. ; Haven't we seen this before?! This *can't* be original! z = 0, zj = pixel: z1 = z*z+pixel z2 = zj*zj+(p1) z = z1+z2 |z| < 4 ;SOURCE: jute.frm } MandelLambda {; Jon Horner ; set co-ords as TLx=-3.0,TLy=3.0,BRx=5.0,BRy=-3.0 -JH Jan 94 ; Fractint uses p1 = (0.5,0.0) ; CAL uses z = (0.01,0.01) with note that z must be >0 ; The Z screen description prior to v18 is wrong: ; (1-z^2) produces a totally different fractal. ; - fixed in v18.0 CAL calls it LogisticEquation. z = (p1), c = pixel: z = z * (1 - z ) * c |z| <= 4 ;SOURCE: parser.frm } MandellambdaPwr {; This provide a "map" for LambdaPwr z = (1/(p1+1))^(1/p1): z = pixel*z*(1 - z^p1) |z| <= 100 ;SOURCE: reb003.frm } MandelLattes (XYAxis) { bailout=real(p2)+100 z=c=pixel: zz=sqr(z) z=c*((zz+2)*zz+1)/(z*(zz-1)) |z|<=bailout ;SOURCE: 99msg.frm } MandelLattesGen (Origin) { bailout=real(p2)+100 z=c=pixel: zz=sqr(z) z=c*fn1(zz+1)/(z*(zz-1)) |z|<=bailout ;SOURCE: 99msg.frm } Mandellike1 (yaxis) {; Peter Anders anders@physik.hu-berlin.de xo=real(p1), yo=imag(p1): x=(xo*xo-yo*yo)*(0,1)+real(pixel) y=2*xo*yo*(0,1)+imag(pixel) z=x+flip(y) xo=x yo=y |fn1(z)|<real(p2) ;SOURCE: peterman.frm } Mandellike10 {; Peter Anders anders@physik.hu-berlin.de xo=0, yo=0, cx=real(pixel), cy=imag(pixel): x=xo*xo-yo*yo+cx y=2*xo*yo+cy xo=fn2(x) yo=fn2(y) |fn1(x)|<real(p2) || |fn1(y)|<real(p2) ;SOURCE: peterman.frm } Mandellike11 {; Peter Anders anders@physik.hu-berlin.de xo=0, yo=0, cx=real(pixel), cy=imag(pixel): x=xo*xo-yo*yo+cx y=2*xo*yo+cy xo=x+p1 yo=y+p1 abs(fn1(x*x+y*y))<real(p2) ;SOURCE: peterman.frm } Mandellike12 {; Peter Anders anders@physik.hu-berlin.de z=(0,0), c=pixel: z=z*z+c z=z^p1 abs(fn1(z))<real(p2) ;SOURCE: peterman.frm } Mandellike13 {; Peter Anders anders@physik.hu-berlin.de z=fn1(pixel), c=fn2(pixel), a=p1, b=p2, d=p3: z=z^a+c^b*z^d z=fn3(z) |z|<100 ;SOURCE: peterman.frm } Mandellike2 (xaxis) {; Peter Anders anders@physik.hu-berlin.de xo=real(p1), yo=imag(p1): x=xo*xo-yo*yo+real(pixel) y=2*xo*yo+imag(pixel) z=x+flip(y) xo=y yo=x |fn1(z)|<real(p2) ;SOURCE: peterman.frm } Mandellike3 {; Peter Anders anders@physik.hu-berlin.de z=p1, c=pixel: z=fn2(z)+c |fn1(z)|<real(p2) ;SOURCE: peterman.frm } Mandellike4 {; Peter Anders anders@physik.hu-berlin.de z=p1, c=pixel: z=fn2(z)*c |fn1(z)|<real(p2) ;SOURCE: peterman.frm } Mandellike5 {; Peter Anders anders@physik.hu-berlin.de z=p1, c=pixel: z=fn2(z)*c+c |fn1(z)|<real(p2) ;SOURCE: peterman.frm } Mandellike6 {; Peter Anders anders@physik.hu-berlin.de z=(0,0), c=fn2(pixel): z=z*z+c |fn1(z)|<real(p2) ;SOURCE: peterman.frm } Mandellike7 {; Peter Anders anders@physik.hu-berlin.de z=(0,0), c=pixel, c=c^real(p1)-imag(p1): z=z*z+c |fn1(z)|<real(p2) ;SOURCE: peterman.frm } Mandellike8 {; Peter Anders anders@physik.hu-berlin.de z=1/pixel, c=pixel: z=z*z+c |fn1(z)|<real(p2) ;SOURCE: peterman.frm } Mandellike9 {; Peter Anders anders@physik.hu-berlin.de z=pixel, c=1/pixel: z=z*z+c |fn1(z)|<real(p2) ;SOURCE: peterman.frm } MandEllipse {; Uses an ellipse rather then a circle for the bailout ; value. real(P1) is the square of it's width, and ; imag(P2) is the square of it's height. z = 0, c = pixel, a = real(p1), b = imag(p1): z = z * z + c real(z) * real(z) / a + imag(z) * imag(z) / b < 1 ;SOURCE: 98msg.frm } MandelLog1 (XAXIS) { c = z = pixel: z = sqr(log(z^z)) + c + p1 |z| <= 4 ;SOURCE: robert.frm } MandelMax {; generalized z^n by Bud 3/27/98 ; probably been done before... ; defaults: p1 = (2,0) p2 = (0,0) p3 = (4,0) z = p2, c = pixel: z = z^p1 + c |z| < p3 ;SOURCE: 98msg.frm } MandelMax2 {; slightly altered by Jim M. ; probably been done before... ; defaults: p1 = (2,0) p2 = (0,0) p3 = (4,0) z = p2, c = pixel, a=p1: z = z^(a) + c |z| < p3 ;SOURCE: 98msg.frm } MandelMaxm {; generalized z^n by Bud 3/27/98 ; probably been done before... ; defaults: p1 = (2,0) p2 = (0,0) p3 = (4,0) IF (p1 == 2) z = p2 ELSE IF (p2 || flip(p2)) z = p2 ELSE z = 1 ENDIF ENDIF c = pixel: z = z^p1 + c |z| < p3 ;SOURCE: test.frm } MandelNone {; edited 5/6/96 for Orgform by George Martin ; Undefined symmetry "(None)" deleted z = Pixel: z = sqr(z) + pixel |z| <= 4 ;SOURCE: newform.frm } mandeloid { ; By PGD, Aug 1997. p2 is bailout, make >4! ; Set p1 small to get normal- ; looking Mandelbrots with subtle mutations. p1=0 gives classic M-set. ; p1>.01 gives a noticeably altered M-set. Large values up to 3 give ; interesting results. Imaginary numbers warp symmetry. ; Replaced variable "e" with "ee" 5/05/99. G. Martin c=pixel, z=c, a=0, b=0, d=0, ee=0, f=0, g=0, h=0, i=0: z=sqr(z)+c+i i=h h=g g=f f=ee ee=d d=b b=a a=z*p1 lastsqr<=p2 ;SOURCE: 97msg.frm } MandelOrigin (ORIGIN) { z = Pixel: z = sqr(z) + pixel |z| <= 4 ;SOURCE: newform.frm } MandelPM {; Jim Muth z=p1+10^(-100), c=pixel: z=p2*((-z)^p3+z^p3)+c |z| <= 250 ;SOURCE: 98msg.frm } MandelPMnew {; Jim Muth z=p2+10^(-100) c=pixel+(p3) a=real(p1)+1, b=imag(p1): z=a*((-z)^b+z^b)+c |z| <= 250 ;SOURCE: 98msg.frm } mandels_galore (xaxis) {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; periodicity=0 must be set ; Try 50 or more for real(p1) - even multiples of ; 256 give interesting effects ; Try 1.2 - 1.8 for imag(p1) ; Try 1000 or more for Maximum Iterations (x menu) z=c=pixel, iter=0 nextzoom = iterspace = real(p1), magnification = imag(p1): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) c = c*(1 - test) + test*magnification*c z = z*z + c iter = iter + 1 |z| <= 16 ;SOURCE: 96msg.frm } mandels_spiral {; Variation on George Martin's mandels_galore formula. ; Sylvie Gallet [101324,3444], 1996 ; periodicity=0 z=c=pixel, iter=0 nextzoom = iterspace = real(p1): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) c = c*(1 - test) + test*(p2*c + p3) z = z*z + c iter = iter + 1 |z| <= 16 ;SOURCE: 96msg.frm } MandelSin1 (XAXIS) { c = z = pixel: z = sqr(z * sin(z)) + c + p1 |z| <= 4 ;SOURCE: robert.frm } MandelSine (XYAXIS) { z = Pixel: z = sin(z) * pixel |z| <= 50 ;SOURCE: fracv13r.frm } MandelTangent {; Fractal Creations example (revised for v.16) z = pixel: z = pixel * tan(z) |real(z)| < 32 ;SOURCE: fractint.frm } MandelVar1 (XAXIS) {; try p1=0.367879441 (= 1/e) c = z = pixel: z = sqr(z) + c + p1 |z| <= 4 ;SOURCE: robert.frm } MandelVar10 (XAXIS) { c = z = pixel: value1 = 1 + p1 value2 = 1 + p2 z = (z^value2)^(value1) + c |z| <= 4 ;SOURCE: robert.frm } MandelVar2 (XAXIS) { c = z = 1 / pixel: z = sqr( sqr(z*c)) + c + p1 |z| <= 4 ;SOURCE: robert.frm } MandelVar3 (XAXIS) {; inverted MandelVar2 c = z = pixel: z = sqr( sqr(z*c)) + c + p1 |z| <= 4 ;SOURCE: robert.frm } MandelVar4 (XAXIS) { c = z = pixel: z = sqr(z) + (1/c) + p1 |z| <= 4 ;SOURCE: robert.frm } MandelVar5 (XAXIS) { c = z = pixel: z = sqr(z*cos(tan(c))) + exp(c) + p1 |z| <= 4 ;SOURCE: robert.frm } MandelVar6 (XAXIS) { c = z = pixel: z = (sqr(1/sin(1+z)+ c))*c + c + p1 |z| <= 4 ;SOURCE: robert.frm } MandelVar7 (XAXIS) { z = pixel: c = log(1+z) z = sqr(z) + c + p1 |z| <= 4 ;SOURCE: robert.frm } MandelVar8 (XAXIS) { c = z = pixel: z = ((z*c)/(z*c+2.718281828)+sin(z))^2 + c |z| <= 4 ;SOURCE: robert.frm } MandelVar9 (XAXIS) { z = pixel: c = z/(z*z+1) z = sin(z^4 + c) + real(c) |z| <= 4 ;SOURCE: robert.frm } MandelXAxis (XAXIS) {; for Transparent3D z = zt ; Define Julia axes as depth/time and the c = xy: ; Mandelbrot axes as width/height for each slice. ; This corresponds to Mandelbrot axes as ; height/depth and the Julia axes as width ; time for the 3D image. z = Sqr(z) + c LastSqr <= 4 ;SOURCE: improved.frm } MandelXY (XYAXIS) { z = Pixel: z = sqr(z) + pixel |z| <= 4 ;SOURCE: newform.frm } MandelY (YAXIS) { z = Pixel: z = sqr(z) + pixel |z| <= 4 ;SOURCE: newform.frm } MandExpGhost {; Ron Barnett, 1998 - modified from Kerry Mitchell ; ; colors Mandelbrot set by combining the smoothed iteration ; with a background of rays from the center ; ; use decomp=256 ; real(p1) = bailout ; imag(p1) = "ghost" adjustment: set to 0 for only ; background rays, try 2 ; calculation performed on variable zc, z used for coloring ; maxr = real(p1), scale = imag(p1)*pi/128 iterexp = 0, iter = 1, zc = 0, c = pixel, background = pixel: iterexp = iterexp + exp(-cabs(zc)), iter = iter + 1, zc = sqr(zc)+c ; ; bailout ; compute smoothed iteration as "angle" ; multiply angle by background to get final z ; set z to background for interior points ; set "iteration done" flag (iter=-1) ; IF ((|zc| > maxr) || (iter == maxit)) smooth = iterexp*scale ang = cos(smooth)+flip(sin(smooth)) z = background*ang IF (iter == maxit) z = background ENDIF iter = -1 ENDIF iter > 0 ;SOURCE: 98msg.frm } MandJulia {; Ron Barnett [70153,1233], 1996 Requires passes=1 ; p3 will shift the julia set wrt the mandelbrot set ; p2 is for the Julia value ; Ron Barnett, 1996 z = pixel+(whitesq==0)*p3 c = whitesq*p1*pixel + (whitesq==0)*p2: z=z*z+c |z|<=4 ;SOURCE: phc.frm } MandK {; Original formula is shown by comment. This is my attempt to ; reconstruct what was intended. George Martin, 5/20/97 ; z^2=w^2=pixel^2: ; z^2*(w^2+z^2)=(p1)^2*(w^2) ; |z|<=1000 z=w=pixel^2 const=p1^2: z=(const*w)/(w+z) |z|<=1000 ;SOURCE: sample.frm } MandKaleido {; Ron Barnett [70153,2133], 1996 ; suggested values: p1 p2 p3 ; 2 slices 1 1 2 ; 3 slices 1 2 3 ; 4 slices 3 2 4 ; 5 slices 4 2 5 ; 6 slices 5 4 6 ; 7 slices 5 4 7 ; 8 slices 6 5 8 ; 9 slices 6 5 9 cr = p1*real(scrnpix) + p2*imag(scrnpix) r = cr - p3 * trunc((cr+0.10) / p3) tpi = 8*atan(1) c = (sin(1/p3*tpi) + flip(cos(1/p3*tpi)))*(r == 0) c1 = (sin(2/p3*tpi) + flip(cos(2/p3*tpi))) * (r == 1) c2 = (sin(3/p3*tpi) + flip(cos(3/p3*tpi))) * (r == 2) c3 = (sin(4/p3*tpi) + flip(cos(4/p3*tpi))) * (r == 3) c4 = (sin(5/p3*tpi) + flip(cos(5/p3*tpi))) * (r == 4) c5 = (sin(6/p3*tpi) + flip(cos(6/p3*tpi))) * (r == 5) c6 = (sin(7/p3*tpi) + flip(cos(7/p3*tpi))) * (r == 6) c7 = (sin(8/p3*tpi) + flip(cos(8/p3*tpi))) * (r == 7) c8 = (sin(9/p3*tpi) + flip(cos(9/p3*tpi))) * (r == 8) c =z = pixel * (c + c1 + c2 + c3 + c4 + c5 + c6 + c7 + c8) : z = z * z + c |z| <= 4 ;SOURCE: reb008.frm } mandlyap {; P1 is the bailout z=0, c=pixel, k=0, l=0, z1=0: z1=z1*z1+c dz1=2*z1 k=k+1 l=l+log(dz1) z=l/k |z1|<=p1 ;SOURCE: 97msg.frm } MandMand { ; Note that floating-point is required to make this compute accurately f=pixel, z=pixel: f=z*z+pixel z=f*f+pixel |f|<=4 ;SOURCE: fractmix.frm } MandMix-x {; Jay Hill u=real(p1), v=imag(p1), w=real(p2), b=4+imag(p2) c=pixel/w, x=v-u, z=(-u/v/w)^(1/x): z=z^u + w*z^v + c |z| <= b ;SOURCE: 98msg.frm } MandMnzpwr {; shit xept p1=2 ; Note that floating-point is required to make this compute accurately f=pixel, z=pixel: f=z^p1+pixel z=f*f+pixel |f|<=4 ;SOURCE: fractmix.frm } MandNewt01 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-(p1*c) b=3*z^2+(p2*c-1) z=z-p3*a/b .00005 <= |a| ;SOURCE: 98msg.frm } MandNewt02 {; Jim Muth z=c=pixel: a=z^p1+(c-1)*z-c b=3*z^p2+c-1 z=z-p3*a/b .000000000000000000000000000001 <= |a| ;SOURCE: 98msg.frm } MandNewt03 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-c b=p1*z^p2+c-1 z=z-p3*a/b .0001 <= |a| ;SOURCE: 97msg.frm } MandNewt04 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-c b=p1*z^2+c-1 z=z-p2*a/b p3 <= |a| ;SOURCE: 98msg.frm } MandNewt05 {; Jim Muth z=c=fn1(pixel): a=z^2+(c-p1)*z-c b=p2*z^2+c-1 z=z-1*a/b p3 <= |a| ;SOURCE: 97msg.frm } MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b .000000000000000000000000000001 <= |a| ;SOURCE: 97msg.frm } MandNewt07 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=3*z^2+c-1 z=z-p3*a/b .000000000000000000000000000001 <= |a| ;SOURCE: 97msg.frm } MandNewt08 {; Jim Muth z=c=(pixel*p1): a=z^p2+(c-1)*z-c b=p3*z^2+c-1 z=z-1*a/b .000000000000000000000000000001 <= |a| ;SOURCE: 98msg.frm } MandNewt09 {; formula, Jim Muth z=c=pixel: a=z^3+(c-1)*z-c b=p1*z^p2+c-1 z=z-1*a/b p3 <= |a| ;SOURCE: 98msg.frm } MandNewt10 {; Jim Muth ; Replaced variable "e" with "ee" 5/05/99. G. Martin z=g=pixel, a=real(p1), b=imag(p1), c=real(p2) d=imag(p2), ee=real(p3), f=imag(p3): h=z^a+(g-b)*z-g j=c*z^d+g z=z-ee*h/j f <= |h| ;SOURCE: 98msg.frm } MandNewt11 {; Jim Muth ; Replaced variable "e" with "ee" 5/05/99. G. Martin z=g=pixel, a=real(p1), b=imag(p1), c=real(p2) d=imag(p2), ee=real(p3), f=imag(p3): h=z^a+(g-b)*z-f j=c*z^d+g z=z-ee*h/j .0000000000000000000000000000005 <= |h| ;SOURCE: 98msg.frm } MandNewt12 {; Jim Muth ; Replaced variable "e" with "ee" 5/05/99. G. Martin z=g=pixel, a=real(p1), b=imag(p1), c=real(p2) d=imag(p2), ee=real(p3), f=imag(p3): h=z^a+(g-1)*(z-b) j=c*z^d+g z=z-ee*h/(f*j) .0000000000000000000000000000005 <= |h| ;SOURCE: 98msg.frm } MandNwtM { ; Note that floating-point is required to make this compute accurately z = pixel, Root = 1: f=z*z+pixel z = ((pixel-1) * f^pixel + Root) / (pixel * f^(pixel-1)) .001 <= |f^pixel - Root| ;SOURCE: fractmix.frm } MandNwtX { ; Note that floating-point is required to make this compute accurately z = pixel, Root = 1: f=z*z+pixel z = ((f-1) * z^f + Root) / (f * z^(f-1)) .001 <= |z^f - Root| ;SOURCE: fractmix.frm } MandOlio { z = pixel : z = z + p1 z = z * fn1(pixel + z) z = sqr(1/z) |z| < 4 ;SOURCE: olio.frm } Mandp1 {; remember to turn on the inside options ; Replaced variable "e" with "ee" 5/05/99. G. Martin z=0, ee=0: ee=sqr(ee)+pixel z=ee-p1 |ee|<=4 ;SOURCE: ramiro.frm } MandPerturb (XAXIS) {; z^2 + c + p3*z try p3(real) = 0.5 or -0.5 z=pixel: z=z*z + pixel + real(p3)*real(z)+imag(p3)*imag(z) |z| <10 ;SOURCE: internet.frm } MandPhoenix {; v18 Based on algorithm by Joyce Haslam - Fractal ; Report iss 16. More details in Roger Steven's book ; `Fractal Programming in C'. Mandelbrot-style map ; of the Phoenix curves. z = (0,0), oldz = (0,0), c = pixel: newz = z * z + real(pixel) + oldz * imag(pixel) oldz = z z = newz |z| <= 4 ;SOURCE: parser.frm } Mandring {; Jim Muth z=p1, c=pixel, d=fn1(c^p2)/p2: z=sqr(z)+d |z| <=p3 ;SOURCE: 98msg.frm } MandTang (XYAXIS) { z = Pixel: z = sin(z) / cos(z) + Pixel |z| <= 4 ;SOURCE: skinv151.frm } Manfn+Exp {; Jon Horner - need to zoom out z = c = pixel : z = fn1(z) + 2.7182818 ^ z + c |z| <= 4 ;SOURCE: parser.frm } ManFn+zsqrd (XAXIS) {; Jon Horner z = c = pixel : z = fn1(z) + (z*z) + c |z| <= 4 ;SOURCE: parser.frm } ManI2I3(XAXIS) { c = z = pixel: q = sqr(z) z = imag(z*q) + flip(imag(q)) + c |z| < 25 ;SOURCE: 97msg.frm } ManI2R3(XAXIS) { c = z = pixel: q = sqr(z) z = real(z*q) + flip(imag(q)) + c |z| < 25 ;SOURCE: 97msg.frm } ManI3I2(YAXIS) {; + c = z = pixel: q = sqr(z) z = imag(q) +flip(imag(z*q)) + c |z| < 25 ;SOURCE: 97msg.frm } ManI3R2 { c = z = pixel: q = sqr(z) z = imag(z*q) +flip(real(q)) + c |z| < 10 ;SOURCE: 97msg.frm } ManInTheOzone (XAXIS_NOPARM) { ; Edited for Fractint v. 20 by George Martin, 10/98 z=p1, x=1: z=sqr(z)+pixel z=cosxx(z)+pixel z=sin(z)+pixel x=x+1 |z|<=4 ;SOURCE: choice.frm } ManInTheOzoneC (XAXIS_NOPARM) { ; Edited for Fractint v. 20 by George Martin, 10/98 z=p1, x=1: IF (x<10) z=sqr(z)+pixel ELSEIF (x<20) z=cosxx(z)+pixel ELSE z=sin(z)+pixel ENDIF x=x+1 |z|<=4 ;SOURCE: choice.frm } ManInTheOzoneC.1 (XAXIS_NOPARM) { ; Edited for Fractint v. 20 by George Martin, 10/98 z=p1, x=1: IF (x<10) z=sqr(z)+pixel ELSEIF (x<20) z=cos(z)+pixel ELSE z=sin(z)+pixel ENDIF x=x+1 |z|<=4 ;SOURCE: choice.frm } manjul_lace {; Requires passes=1 George Martin, 1996 ; Modified for IF..ELSE logic by Sylvie Gallet, March 1997 ; If Real(p1) is: ; 0 : formula draws PHC manjul_lace ; 1 : formula draws mandel component only ; 2 : formula draws julia component only IF (p1==1 || p1 == whitesq) z = c = 1.5*pixel ELSE z = pixel, c = (-.75, .1234567) ENDIF : z = z*z + c |z| <= 4 ;SOURCE: ifs196.frm } Manlam[Fn||Fn] {; v18 - Jonathan Osuch ; This one doesn't work quite right, I don't know why. ; Note: use floating point ; Edited for Fractint v. 20 by George Martin, 10/98 z = p1, shift = real(p2), x = |z| : IF (x<shift) z=pixel*fn1(z) ELSE z=pixel*fn2(z) ENDIF x=|z| x<=64 ;SOURCE: parser.frm } ManMiIa { z=0 c=pixel: z=sqr(z) z=z+c-abs(imag(z)) |z| <=4 ;SOURCE: crocker.frm } ManMiIaJ (ORIGIN) { z=pixel c=P1: z=sqr(z) z=z+c-abs(imag(z)) |z| <=4 ;SOURCE: crocker.frm } ManMiIm {; Compare Crescent z=0 c=pixel: z=sqr(z) z=z+c-imag(z) |z| <=4 ;SOURCE: crocker.frm } ManMiImJ (ORIGIN) { z=pixel c=P1: z=sqr(z) z=z+c-imag(z) |z| <=4 ;SOURCE: crocker.frm } ManMinusN-XZ { z=real(pixel)+flip(real(p1)) c=imag(pixel)+flip(imag(p1)): z=(-z)^p2+(p3*c) |z| <= 16 ;SOURCE: 97msg.frm } ManMinusN-YZ { z=real(pixel)+flip(real(p1)) c=flip(imag(pixel))+imag(p1): z=(-z)^p2+(p3*c) |z| <= 16 ;SOURCE: 97msg.frm } ManMiRe (XAXIS) {; Compare Crescent z=0 c=pixel: z=sqr(z) z=z+c-real(z) |z| <=16 ;SOURCE: crocker.frm } ManMiReJ (ORIGIN) { z=pixel c=P1: z=sqr(z) z=z+c-real(z) |z| <=16 ;SOURCE: crocker.frm } ManN-2-pro-YW {; Jim Muth z=real(p1)+flip(real(pixel)) g=imag(p1)+flip(imag(pixel)) a=real(p2), b=imag(p2), c=real(p3), d=imag(p3): z=(a*(z^b))+(c*(z^d))+g |z| <= 16 ;SOURCE: 97msg.frm } ManN-XW-YW {; Jim Muth, Thanks to Benno ; p3 = 0 = Julibrot XW plane ; p3 = 1 = Julibrot YW plane ; p3 = >0 <1 = Oblique planes z=flip(real(pixel))+real(p1) c=flip(imag(pixel))+imag(p1) a=p3, b=flip(cos(asin(p3))): z=z^p2+((a+b)*c) |z| <= 25 ;SOURCE: frac_art.frm } ManN-YW {; Jim Muth z=real(p1)+flip(real(pixel)) c=imag(p1)+flip(imag(pixel)): z=z^p2+(p3*c) |z| <= 16 ;SOURCE: 97msg.frm } ManN-YWa {; Jim Muth z=real(p1)+flip(real(pixel)) c=imag(p1)+flip(imag(pixel)): z=z^p2+(p3*c) |z| <= 16 ;SOURCE: 0from_ml.frm } ManN-YZ { z=real(pixel)+flip(real(p1)) c=flip(imag(pixel))+imag(p1): z=z^p2+(p3*c) |z| <= 16 ;SOURCE: 97msg.frm } ManN-YZ-XZ {; Jim Muth, Thanks to Benno ; p3 = 0 = Julibrot YZ plane ; p3 = 1 = Julibrot XZ plane ; p3 = >0 <1 = Oblique planes z=real(pixel)+flip(real(p1)) c=imag(pixel)+flip(imag(p1)) a=p3, b=flip(cos(asin(p3))): z=z^p2+((a+b)*c) |z| <= 25 ;SOURCE: 97msg.frm } manowar {; Chuck Ebbert added 12 Jan 1993 ; p1=initial perturbation of z ; bailout is real(p2) (default 4) z = pixel + p1, z1=z, c=pixel t = (4 * (real(p2)<=0) + real(p2) * (0<p2) ): oldz = z z = sqr(oldz) + z1 + c z1 = oldz |z| <= t ;SOURCE: builtn2.frm } manowarj {; Chuck Ebbert added 12 Jan 1993 ; p1 = Parameter c ; bailout is real(p2) (default 4) z = pixel, z1 = z, c = p1 t = (4 * (real(p2)<=0) + real(p2) * (0<p2) ): oldz = z z = sqr(oldz) + z1 + c z1 = oldz |z| <= t ;SOURCE: builtn2.frm } ManPlIa {; Intended to be same as Slippery Slope z=0 c=pixel: z=sqr(z) z=z+c+abs(imag(z)) |z| <=4 ;SOURCE: crocker.frm } ManPlIaJ (ORIGIN) { z=pixel c=P1: z=sqr(z) z=z+c+abs(imag(z)) |z| <=4 ;SOURCE: crocker.frm } ManPlIm2 { z=0 c=pixel: z=sqr(z) z=z+imag(z)+c |z| <=4 ;SOURCE: crocker.frm } ManPlImJ (ORIGIN) { z=pixel c=P1: z=sqr(z) z=z+c+imag(z) |z| <=4 ;SOURCE: crocker.frm } ManPlP { z=0 c=pixel: z=sqr(z) z=z+c+real(c) |z| <=4 ;SOURCE: crocker.frm } ManPlQ { z=0 c=pixel: z=sqr(z) z=z+c+imag(c) |z| <=4 ;SOURCE: crocker.frm } ManPlRa { z=0 c=pixel: z=sqr(z) z=z+c+abs(real(z)) |z| <=4 ;SOURCE: crocker.frm } ManPlRaJ (ORIGIN) { z=pixel c=P1: z=sqr(z) z=z+c+abs(real(z)) |z| <=4 ;SOURCE: crocker.frm } ManPlRe {; Compare Cresent z=0 c=pixel: z=sqr(z) z=z+c+real(z) |z| <=4 ;SOURCE: crocker.frm } ManPlReJ (ORIGIN) {; Compare Cresent z=pixel c=P1: z=sqr(z) z=z+c+real(z) |z| <=4 ;SOURCE: crocker.frm } ManR2I3(XAXIS) { c = z = pixel: q = sqr(z) z = real(q) + flip(imag(z*q)) + c |z| < 10 ;SOURCE: 97msg.frm } ManR2R3(XYAXIS) { c = z = pixel: q = sqr(z) z = real(z*q) + flip(real(q)) + c |z| < 10 ;SOURCE: 97msg.frm } ManR3I2 { c = z = pixel: q = sqr(z) z = imag(q) + flip(real(z*q)) + c |z| < 25 ;SOURCE: 97msg.frm } ManR3R2(XAXIS) { c = z = pixel: q = sqr(z) z = real(q) +flip(real(z*q)) + c |z| < 10 ;SOURCE: 97msg.frm } Mans-G+SG-3-03 {; Test Variation on Sylvie Gallet formula z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y))* (whitesq == 0) + c * whitesq y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) c = c*(1 - test) + test*magnification*c z = (z+ x1+flip(y1))*z+c iter = iter + 1 |z| <= 16 ;SOURCE: bj-phc02.frm } Mans-G+SG-3-03b {; Test Variation on Sylvie Gallet formula z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y))* (whitesq == 0) + c * whitesq y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) c = c*(1 - test) + test*magnification*c z = (x1+flip(y1)) * (whitesq == 0) + (z*z + c) * whitesq iter = iter + 1 |z| <= 16 ;SOURCE: bj-phc02.frm } mans-galore-011 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel/(1.0,0.1), iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)) z = z*(1 - test) + x1+flip(y1) c = c*(1 - test) + test*magnification*c z = z*z + c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-012 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + x1+flip(y1) c = c*(1 - test) + test*magnification*c z = z*z + c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-013 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + x1+flip(y1) z = z*(1 - test) + y1+flip(x1) c = c*(1 - test) + test*magnification*c z = z*z + c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-018 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 ; Revised for Fractint v20 by G. Martin z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + x1+flip(y1) c = c*(1 - test) + test*magnification*c z = z*z + c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-019 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + x1+flip(y1) c = c*(1 - test) + test*magnification*c z = fn3(z)*fn4(z)+c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-020 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + x1+flip(y1) c = c*(1 - test) + test*magnification*c z = fn3(z*z+c) iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-021 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + y1+flip(x1) c = c*(1 - test) + test*magnification*c z = fn3(z*z+c) iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-022 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + y1+y1+flip(x1+x1) c = c*(1 - test) + test*magnification*c z = fn3(z*z+c) iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-024 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + fn4(x1+flip(y1)) c = c*(1 - test) + test*magnification*c z = fn3(z)*z+c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-027 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + fn3(x1)+flip(fn4(y1)) c = c*(1 - test) + test*magnification*c z = z*z+c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-029 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(fn3(y))) y1 = y - p2*fn1(x+p3*fn2(fn3(x))): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + fn4(x1)+flip(fn4(y1)) c = c*(1 - test) + test*magnification*c z = z*z+c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-032 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z=c=pixel, iter=0, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + fn3(x1)+sqr(flip(fn4(y1))) c = c*(1 - test) + test*magnification*c z = z*z+c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-036 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z = pixel, c = pixel, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + fn3(x1)/flip(fn4(y1)) c = c*(1 - test) + test*magnification*c z = z*z+c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } mans-galore-037 {; Variation on Sylvie Gallet formula. ; George Martin [76440,1143] ; Modified Mans-Galore & Gallet 3-02 z = pixel, c = pixel, x = real(z), y = imag(z) nextzoom = iterspace = real(p1), magnification = imag(p1) x1 = x - p2*fn1(y+p3*fn2(y)) y1 = y - p2*fn1(x+p3*fn2(x)): test = (iter == nextzoom) nextzoom = nextzoom + test*iterspace z = z*(1 - test) + fn3(x1)*flip(fn4(y1)) c = c*(1 - test) + test*magnification*c z = z*z+c iter = iter + 1 |z| <= 16 ;SOURCE: bej011.frm } ManTest1XY-XZ { z=real(pixel)+(p1*(imag(pixel)))+flip(real(p2)) c=imag(pixel)+(p1*(real(pixel)))+flip(imag(p2)): z=z^p3+c |z| <= 16 ;SOURCE: 97msg.frm } mantle {; Giuseppe Zito z = pixel c0 = real(p1) IF (real(p1)==0) c0 = -0.614927 ENDIF : x = real(z), y = imag(z) newx = c0 + y newy = x*x - y z = newx + flip(newy) newx < 4 && newx > -4 && newy < 4 && newy > -4 ;SOURCE: zg.frm } Mantura (XAXIS) { z = pixel, sspix = sqr(sin(pixel)): z = z * sspix + p1 z = z * z + pixel |z| < 4 ;SOURCE: altura.frm } Mantura_2 (XAXIS) { z = pixel, sspix = sin(sqr(pixel)): z = z * sspix + p1 z = z * z + pixel |z| < 4 ;SOURCE: altura.frm } many_man {; Modified Stephen C. Ferguson formula ; adapted for Fractint by Les St Clair, 1997 ; use real p1 to set bailout (try p1=4) ; use real p2 to set number of mandels ; set fn1=ident, fn2=log for "default" formula z=0, c=pixel: z=(z*z)+fn1(fn2(c^p2)/p2) |z| <=p1 ;SOURCE: many_man.frm } many_man_phc {; Modified Stephen C. Ferguson formula ; adapted for Fractint by Les St Clair, 1997 ; phc variation by P. DiGiorgi ; use imag(p1) to set bailout z=0, c1=fn3(pixel), c0=fn4(pixel) IF (whitesq) v = (c1^p2)/p2 ELSE v = (c0^p2)/p2 ENDIF n = p3*fn1(fn2(v)): z = z^(real(p1)) + n |z| <= imag(p1) ;SOURCE: 97msg.frm } Many_mods {; Linda Allison May 15,1997 ; modified by Sylvie Gallet ; modified again by Linda Allison ; and again by David Shanholtzer ; 1st parameter: real(p1) = bailout ; 2nd parameter: imag(p1) = number of sides z=0 c=0.4*log(sqr(pixel^imag(p1))): z2=fn1(z)+c sqz2=fn2(z2) z=c*(1-sqz2)/(1+sqz2) |z| <= p1 ;SOURCE: 98msg.frm } ManzanaJ {; ao950@FreeNet.Carleton.CA (Paul Derbyshire) ; Use floating point, this one is weird.} z=pixel, c=p1: z=sin(z)/(z*z*z-z)+c |z|>0.000001 ;SOURCE: manzanaj.frm } ManzNwt { ; Note that floating-point is required to make this compute accurately z = pixel, Root = 1: f=z^p2+pixel z = ((p1-1) * f^p1 + Root) / (p1 * f^(p1-1)) .001 <= |f^p1 - Root| ;SOURCE: fractmix.frm } manzpower {; Chuck Ebbert added 12 Jan 1993 ; p1 = initial perturbation of z ; p2 = exponent (default 2) ; bailout fixed at 4 z = pixel + p1, c = pixel ex = (2 * (|p2|<=0) + p2 ): z = z^real(ex) + c ; should be real(int(ex)) 13 Jan 1993 |z| <= 4 ;SOURCE: builtn2.frm } manzzpwr {; Chuck Ebbert added 12 Jan 1993 ; p1 = initial perturbation of z ; p2 = exponent (default 2) ; bailout fixed at 4 z = pixel + p1, c = pixel ex = (2 * (|p2|<=0) + p2 ): z = z^z + z^real(ex) + c ; should be real(int(ex)) 13 Jan 1993 |z| <= 4 ;SOURCE: builtn2.frm } MarksJulia (ORIGIN) {; Jon Horner/Jonathan Osuch - Jun 1994 ; set p1 = (0.1,0.9), p2 = 1 ; if you want to vary both real and imag ; parts of exponent use CmplxMarksJul z = pixel, c = p1, one = (1,0) : z = (c ^ (real(p2)-one)) * sqr(z) + c |z| <= 4 ;SOURCE: parser.frm } MarksMandel (XAXIS) {; Jon Horner/Jonathan Osuch - Jun 1994 ; if you want to vary both real and imag ; parts of exponent use CmplxMarksMand z = pixel + p1, c = pixel, one=(1,0) : z = (c ^ (real(p2)-one)) * sqr(z) + c |z| <= 4 ;SOURCE: parser.frm } MarksMandelPwr (XAXIS) { z = pixel, c = z ^ (z - 1): z = c * sqr(z) + pixel |z| <= 4 ;SOURCE: newform.frm } MarksMandelPwr_tan (XAXIS) { z = pixel, c = z ^ (z - 1): z = c * sin(z)/cos(z) + pixel |z| <= 4 ;SOURCE: formulas.frm } marlinZZa (XAXIS) {; Prof Jm using Newton-Raphson method ; use floating point with this one z=pixel, solution=1: z1=z^(z-1) z2=(((z-1)/z)+log(z))*z1 z=z-((z1-1)/z2) 0.05 <= |solution-z1| ;SOURCE: davfav1.frm } Mask {; Ron Barnett, 1993 ; try fn1 = log, fn2 = sinh, fn3 = cosh ; P1 = (0,1), P2 = (0,1) ; Use floating point z = fn1(pixel): z = P1*fn2(z)^2 + P2*fn3(z)^2 + pixel |z| <= 4 ;SOURCE: fractint.frm } master {; Giuseppe Zito z = pixel c1 = 0.688383 c2 = -0.257283 c4 = 0.259209 d0 = 0.004197 d3 = 0.93075 d5 = 0.210723 : x = real(z), y = imag(z) s0 = x s0 = s0 *c1 s0 = s0 *c2 s1 = y s1 = s1 +c4 s0 = s0 +s1 newx = s0 s0 =d0 s0 = s0 *x s0 = s0 *d3 s0 = s0 /y s0 = s0 -d5 s0 = s0 -x newy = s0 z = newx + flip(newy) newx < 4 && newx > -4 && newy < 4 && newy ;SOURCE: zg.frm } matress {; Giuseppe Zito z = pixel c2 = 0.68162298 c8 = 0.96401101 d1 = -0.95945197 d5 = -0.458745 d12 = -0.425805 d15 = -0.36000001 : x = real(z), y = imag(z) s0 = y s0 = s0 /c2 s0 = s0 *y s0 = s0 *y s0 = s0 -y s0 = s0 *c8 newx = s0 s0 = y s0 = s0 /d1 s0 = s0 +y s0 = s0 *y s0 = s0 -d5 s0 = s0 -y s0 = s0 +y s1 =d12 s1 = s1 *x s1 = s1 /x s1 = s1 -d15 s0 = s0 *s1 s0 = s0 /x s0 = s0 -y s0 = s0 +x s0 = s0 +y newy = s0 z = newx + flip(newy) newx < 4 && newx > -4 && newy < 4 && newy > -4 ;SOURCE: zg.frm } Matsch^-1 {; davon ist der K-Matsch die Julia-Menge Grund=pixel+1/(fn1(p2*pixel)-p1)+1/(fn2(p2*pixel)-p1) z=Grund: z=((Grund-1)*z^Grund+1)/(Grund*z^(Grund-1)) 0.001<=|z^Grund-1| ;SOURCE: crazynwt.frm } May {; Sylvie Gallet, Dec 1997 ; Newton's method applied to z^3 - 1 = 0 ; Coloring algorithm by Scott Burns ; Use decomp = 256 and periodicity = 0 z1 = pixel, iter = 0 a = p1*(0,0.0245436) ; real(p1) * 2i pi / 256 : mz = cabs(z1) z2 = z1*z1 z1 = ((2.5,-0.7)*z1*z2 + (0.5,0.7)) / (3*z2) dz = abs(abs(real(z1)-0.25)-0.75) IF (dz <= 0.1) z = exp((iter + 10*dz)*a) cont = 0 ELSEIF (mz <= 0.25) z = exp((256/p1-1 + 4*mz)*a), cont = 0 ELSE iter = iter + 1, cont = 1 ENDIF cont ;SOURCE: 97msg.frm } May-2 {; Sylvie Gallet, Dec 1997 ; Newton's method applied to z^3 - 1 = 0 ; Use decomp = 256 and periodicity = 0 z1 = pixel, iter = 0, j = -0.5 + flip(sqrt(0.75)), k = conj(j) a = p1*(0,0.0245436) ; real(p1) * 2i pi / 256 : mz = cabs(z1) z2 = z1*z1 z1 = ((2.5,-0.7)*z1*z2 + (0.5,0.7)) / (3*z2) dz = abs(real(z1+0.5)) IF (dz > 0.1) dz = abs(real(z1*j+0.5)) IF (dz > 0.1) dz = abs(real(z1*k+0.5)) ENDIF ENDIF IF (dz <= 0.1) z = exp((iter + 10*dz)*a), cont = 0 ELSEIF (mz <= 0.25) z = exp((256/p1-1 + 4*mz)*a), cont = 0 ELSE iter = iter + 1, cont = 1 ENDIF cont ;SOURCE: 98msg.frm } mc { z=0, c=pixel: z=sqr(z)+c c=c+p1*c |z| <= 4 ;SOURCE: explode.frm } MConj_Maxi(XAXIS) {; an automatic Mix z = a = pixel b = conj(pixel) IF(p1==0) bailout=8 ELSE bailout = |p1| ENDIF: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = v ELSE z = u ENDIF |z|<bailout ;SOURCE: 97msg.frm } MConj_Mini(XAXIS) {; an automatic Mix z = a = pixel b = conj(pixel) IF(p1==0) bailout=8 ELSE bailout = |p1| ENDIF: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = u ELSE z = v ENDIF |z|<bailout ;SOURCE: 97msg.frm } MDRAG (XAXIS) { z=.5 c=pixel: z=c*z*(1-z) |z| <=4 ;SOURCE: crocker.frm } medusa {; Giuseppe Zito (132) z=pixel, a=0.598459, b=-0.063717: x = real(z), y = imag(z) newx = (x*y + a*x)/(y+b) newy = x*x/y - x*x z = newx + flip(newy) (newx < 4) && (newx > -4) && (newy < 4) && (newy > -4) ;SOURCE: zg.frm } merryxms_01 {; Les St Clair [101461.2032@compuserve.com] December 1996 ; Fractint formula containing "Merry Christmas" text, based on ; Jim Deutch's snowflake "JDFrmF23.frm" and modified using ; FracText 1.0 (alpha 5b) by Jan Maarten van der Valk ; 'periodicity=0' and 'passes=1' recommended x=real(scrnpix)/real(scrnmax) y=(imag(scrnmax)-imag(scrnpix))/real(scrnmax), z=x+flip(y) xm=2.5*x chrM1 = (y<-xm+1.2086||y<xm-0.24556)&&y>-xm+1.14223&&y>xm-0.31193||(x>0.\ 23889&&x<0.26354)||(x>0.31812&&x<0.34277) chrE2 = x<0.37467||y<0.42465||(y<0.48482&&y>0.46018)||y>0.52035&&x>0.350\ 02&&x<0.43267 xr=2*x chrR3 = y<0.48482&&y>0.46018||y>0.52035||x<0.46457&&x>0.43992&&x<0.49357\ ||(abs(cabs(z+(-0.49357,-0.50259))-0.03009)<0.01232&&x>0.49357)||(y<0.47\ 25&&y<-xr+1.47197&&y>-xr+1.41685) chrR4 = y<0.48482&&y>0.46018||y>0.52035||x<0.56789&&x>0.54324&&x<0.59689\ ||(abs(cabs(z+(-0.59689,-0.50259))-0.03009)<0.01232&&x>0.59689)||(y<0.47\ 25&&y<-xr+1.6786&&y>-xr+1.62348) xy=2*x chrY5 = y<xy-0.9221&&y>xy-0.97722||(y>-xy+1.8381&&y<-xy+1.89322)&&y>xy-0\ .97722 test1 = chrM1||chrE2||chrR3||chrR4||chrY5&&y>0.4&&y<0.545 xc=1*x chrC6 = abs(cabs(z+(-0.1282,-0.2125))-0.06018)<0.01232&&(x<0.1282||y>xc+\ 0.0843||y<-xc+0.3407) chrH7 = x<0.21136||x>0.25486||(y<0.22482&&y>0.20018)&&x>0.18671&&x<0.279\ 51 chrR8 = y<0.22482&&y>0.20018||y>0.26035||x<0.31141&&x>0.28676&&x<0.34041\ ||(abs(cabs(z+(-0.34041,-0.24259))-0.03009)<0.01232&&x>0.34041)||(y<0.21\ 25&&y<-xr+0.90565&&y>-xr+0.85053) chrI9 = x>0.39007&&x<0.41472 chrS10 = abs(cabs(z+(-0.46439,-0.24259))-0.03009)<0.01232&&(x<0.46439||y\ >0.24259)||(abs(cabs(z+(-0.46439,-0.18241))-0.03009)<0.01232&&(x>0.46439\ ||y<0.18241)) chrT11 = y>0.26035&&x>0.51405&&x<0.6112||(x>0.5503&&x<0.57495) chrM12 = (y<-xm+1.89749||y<xm-1.45445)&&y>-xm+1.83112&&y>xm-1.52083||(x>\ 0.61845&&x<0.6431)||(x>0.69768&&x<0.72233) xa=3*x chrA13 = y>xa-2.12669||y>-xa+2.61874||(y<0.198&&y>0.17335)&&y<xa-2.04874\ &&y<-xa+2.69669 chrS14 = abs(cabs(z+(-0.90189,-0.24259))-0.03009)<0.01232&&(x<0.90189||y\ >0.24259)||(abs(cabs(z+(-0.90189,-0.18241))-0.03009)<0.01232&&(x>0.90189\ ||y<0.18241)) test2 = chrC6||chrH7||chrR8||chrI9||chrS10||chrT11||chrM12||chrA13||chrS\ 14&&y>0.14&&y<0.285 test0=test1||test2 ; Import of formula 'JDFrmF23' from file JDFLAKE.FRM cr = real(scrnpix) + imag(scrnpix) r = cr - 3 * trunc(cr / real(3)) sq3 = 0.5 + flip(sqrt(3)/2) c = (r == 0) + sq3*(r == 1) + conj(sq3)*(r == 2) z =c*pixel: z=z*z+p1 |z|<4&&test0==0 ;SOURCE: 96msg.frm } merryxms_02 {; Les St Clair [101461.2032@compuserve.com] December 1996 ; Fractint formula containing "Merry Christmas" text, based on ; Jo Weber's ComplexNewton_01.frm and modified using ; FracText 1.0 (alpha 5b) by Jan Maarten van der Valk ; modified 12/1998 by JoWeber ; 'periodicity=0' and 'passes=1' recommended x=real(scrnpix)/real(scrnmax) y=(imag(scrnmax)-imag(scrnpix))/real(scrnmax), z=x+flip(y) xm=2.5*x chrM1 = (y<-xm+1.2086||y<xm-0.24556)&&y>-xm+1.14223&&y>xm-0.31193||(x>0.\ 23889&&x<0.26354)||(x>0.31812&&x<0.34277) chrE2 = x<0.37467||y<0.42465||(y<0.48482&&y>0.46018)||y>0.52035&&x>0.350\ 02&&x<0.43267 xr=2*x chrR3 = y<0.48482&&y>0.46018||y>0.52035||x<0.46457&&x>0.43992&&x<0.49357\ ||(abs(cabs(z+(-0.49357,-0.50259))-0.03009)<0.01232&&x>0.49357)||(y<0.47\ 25&&y<-xr+1.47197&&y>-xr+1.41685) chrR4 = y<0.48482&&y>0.46018||y>0.52035||x<0.56789&&x>0.54324&&x<0.59689\ ||(abs(cabs(z+(-0.59689,-0.50259))-0.03009)<0.01232&&x>0.59689)||(y<0.47\ 25&&y<-xr+1.6786&&y>-xr+1.62348) xy=2*x chrY5 = y<xy-0.9221&&y>xy-0.97722||(y>-xy+1.8381&&y<-xy+1.89322)&&y>xy-0\ .97722 test1 = chrM1||chrE2||chrR3||chrR4||chrY5&&y>0.4&&y<0.545 xc=1*x chrC6 = abs(cabs(z+(-0.1282,-0.2125))-0.06018)<0.01232&&(x<0.1282||y>xc+\ 0.0843||y<-xc+0.3407) chrH7 = x<0.21136||x>0.25486||(y<0.22482&&y>0.20018)&&x>0.18671&&x<0.279\ 51 chrR8 = y<0.22482&&y>0.20018||y>0.26035||x<0.31141&&x>0.28676&&x<0.34041\ ||(abs(cabs(z+(-0.34041,-0.24259))-0.03009)<0.01232&&x>0.34041)||(y<0.21\ 25&&y<-xr+0.90565&&y>-xr+0.85053) chrI9 = x>0.39007&&x<0.41472 chrS10 = abs(cabs(z+(-0.46439,-0.24259))-0.03009)<0.01232&&(x<0.46439||y\ >0.24259)||(abs(cabs(z+(-0.46439,-0.18241))-0.03009)<0.01232&&(x>0.46439\ ||y<0.18241)) chrT11 = y>0.26035&&x>0.51405&&x<0.6112||(x>0.5503&&x<0.57495) chrM12 = (y<-xm+1.89749||y<xm-1.45445)&&y>-xm+1.83112&&y>xm-1.52083||(x>\ 0.61845&&x<0.6431)||(x>0.69768&&x<0.72233) xa=3*x chrA13 = y>xa-2.12669||y>-xa+2.61874||(y<0.198&&y>0.17335)&&y<xa-2.04874\ &&y<-xa+2.69669 chrS14 = abs(cabs(z+(-0.90189,-0.24259))-0.03009)<0.01232&&(x<0.90189||y\ >0.24259)||(abs(cabs(z+(-0.90189,-0.18241))-0.03009)<0.01232&&(x>0.90189\ ||y<0.18241)) test2 = chrC6||chrH7||chrR8||chrI9||chrS10||chrT11||chrM12||chrA13||chrS\ 14&&y>0.14&&y<0.285 test0=test1||test2 ; Import of formula pr = 1/p1, pm1 = 1-pr, pm2 = 1-p1, z = pixel : oldz = z z = pm1 * z + pr * z^pm2 |(z-oldz)|>=0.000001&&test0==0 ;SOURCE: 98msg.frm } mfn2fn { z=pixel: power = fn2(z) z = fn1(z)^power + pixel |z| < p2 ;SOURCE: fractals.frm } mfnc { z=0, c=pixel: z=sqr(z)+c c=c+p1*fn1(c) |z| <= 4 ;SOURCE: explode.frm } mfnz { z=0, c=pixel: z=sqr(z)+c c=c+p1*fn1(z) |z| <= 4 ;SOURCE: explode.frm } MGen_Maxi {; generalized Minimax-Set ; (p1 and p2 may not both be 0!) ; p1 = (-1,0) and p2 = (0,-1) gives Mpm ; p1 = (1,0) and p2 = (0,-1) gives MConj ; p1 = (-1,0) and p2 = (0,1) gives MXConj IF(p1==0) IF(p2==0) p1 = -1 p2 = flip(-1) ; use Mpm as default ENDIF ENDIF z = a = pixel ra = real(a) ia = imag(a) b = real(p1)*ra + real(p2)*ia + flip(imag(p1)*ra+imag(p2)*ia) IF(p3==0) bailout=8 ELSE bailout = |p3| ENDIF: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = v ELSE z = u ENDIF |z|<=bailout ;SOURCE: 97msg.frm } MGen_Mini {; generalized Minimax-Set ; (p1 and p2 may not both be 0!) ; p1 = (-1,0) and p2 = (0,-1) gives Mpm ; p1 = (1,0) and p2 = (0,-1) gives MConj ; p1 = (-1,0) and p2 = (0,1) gives MXConj IF(p1==0) IF(p2==0) p1 = -1 p2 = flip(-1) ; use Mpm as default ENDIF ENDIF z = a = pixel ra = real(a) ia = imag(a) b = real(p1)*ra + real(p2)*ia + flip(imag(p1)*ra+imag(p2)*ia) IF(p3==0) bailout=8 ELSE bailout = |p3| ENDIF: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = u ELSE z = v ENDIF |z|<=bailout ;SOURCE: 97msg.frm } Mi_Maxi {; an automatic Mix z = a = pixel b = (0,1) * pixel IF(p1==0) bailout=8 ELSE bailout = |p1| ENDIF: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = v ELSE z = u ENDIF |z|<=bailout ;SOURCE: 97msg.frm } Mi_Mini {; an automatic Mix z = a = pixel b = (0,1) * pixel IF(p1==0) bailout=8 ELSE bailout = |p1| ENDIF: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = u ELSE z = v ENDIF |z|<=bailout ;SOURCE: 97msg.frm } Michaelbrot (origin) {; based on Golden Mean z = pixel: z = sqr(z) + ((sqrt 5 + 1)/2) |z| <= 4 ;SOURCE: drcha.frm } MikeTan (XAXIS) {; Mike Traynor c = z = pixel: z = z*tan(z) + c |z| <= 4 ;SOURCE: fract182.frm } Mind_2 { ; These formulas were developed after having read ; COMPUTERS AND THE IMAGINATION [Chapter 27] Turning ; a Universe Inside-Out. This is just a new venture ; and I am still exploring this rich area. ; This Fractint .FRM file (c) 1993 by: ; LRCMIKE@LRC.OLDSCOLLEGE.AB.CA ; Michael G. Wareman ; P.O. Box 1856 ; Olds, Alberta, Canada ; T0M 1P0 z = c = pixel: z = c * sin(1 / z) |z| <= 100 ;SOURCE: physics.frm } Mind_3 { ; This Fractint .FRM file (c) 1993 by: ; LRCMIKE@LRC.OLDSCOLLEGE.AB.CA ; Michael G. Wareman ; P.O. Box 1856 ; Olds, Alberta, Canada ; T0M 1P0 z = c = pixel: z = c * sin(1 / z) z = z * z + c |z| <= 4 ;SOURCE: physics.frm } Mind_4 { ; This Fractint .FRM file (c) 1993 by: ; LRCMIKE@LRC.OLDSCOLLEGE.AB.CA ; Michael G. Wareman ; P.O. Box 1856 ; Olds, Alberta, Canada ; T0M 1P0 z = c = pixel z = c * sin(1 / z): z = z * z + c |z| <= 4 ;SOURCE: physics.frm } Mind_5 { ; This Fractint .FRM file (c) 1993 by: ; LRCMIKE@LRC.OLDSCOLLEGE.AB.CA ; Michael G. Wareman ; P.O. Box 1856 ; Olds, Alberta, Canada ; T0M 1P0 z = c = pixel: z = c * sin(1 / z) z = z * z |z| <= 100 ;SOURCE: physics.frm } Mine-10-2-2 {; Linda Allison z = pixel, c = z ^ z: z2 = (pixel ^ (z + 1)) + (fn1(p1))/3 z = z2/p1 + c - z2 |z| <= p2 + 3 ;SOURCE: abpf96.frm } MiniSanMarco1 { z = pixel, c = (-0.1613432317972183, 1.036044612526894) z = z*z + c |z| < 4 ;SOURCE: 99msg.frm } minmaxc_jul {; Kerry Mitchell ; colors the screen one color if the iterate falls between the ; high and low bounds, otherwise leaves it blank ; Julia set--c=p1, bailout=real(p2) ; low and high bounds are set through p3-- ; center of range = real(p3)*|c| (try 1) ; width of range = imag(p3) (try 0.05) ; color with single-pass mode and decomp zc=pixel, c=p1, r=real(p2), z=1 rc=|c|, k1=real(p3)*rc, k2=imag(p3)*0.5 lo=k1*(1-k2), hi=k1*(1+k2): zc=sqr(zc)+c, rzc=|zc| IF ((rzc>lo)&&(rzc<hi)) z=-1 ENDIF rzc < r ;SOURCE: 98msg.frm } minmaxc_man {; Kerry Mitchell lkmitch@primenet.com ; minmaxc_jul as mandelized by Mike Traynor ; colors the screen one color if the iterate falls between the ; high and low bounds, otherwise leaves it blank ; Mandel set--c=pixel, bailout=real(p1) ; low and high bounds are set through p3-- ; center of range = real(p2)*|c| (try 1) ; width of range = imag(p2) (try 0.05) ; color with single-pass mode and decomp zc=c=pixel, r=real(p1), z=1 rc=|c|, k1=real(p2)*rc, k2=imag(p2)*0.5 lo=k1*(1-k2), hi=k1*(1+k2): zc=sqr(zc)+c, rzc=|zc| IF ((rzc>lo)&&(rzc<hi)) z=-1 ENDIF rzc < r ;SOURCE: fraclist.frm } minN-XY-XWrot {; Jim Muth, thanks to Benno Schmid ; real(p1)=rotation angle in degrees, imag(p1)=power of Z ; p2 and p3=rotation point and parallel planes a=real(p1), b=imag(p1) z=sin(a*.01745329251994)*flip(imag(pixel))+p2 c=cos(a*.01745329251994)*flip(imag(pixel))+real(pixel)+p3: z=(-z)^b+c |z| <= 16 ;SOURCE: 97msg.frm } minN-XY-YWrot {; Jim Muth M to R rotation ; real(p1)=rotation angle in degrees, imag(p1)=power of Z ; p2 and p3 rotation point and parallel planes a=real(p1), b=imag(p1) z=sin(a*.01745329251994)*flip(real(pixel))+p2 c=cos(a*.01745329251994)*real(pixel)+flip(imag(pixel))+p3: z=(-z)^b+c |z| <= 16 ;SOURCE: 98msg.frm } minN-XY-YZrot {; Jim Muth, thanks to Benno ; real(p1)=rotation angle in degrees, imag(p1)=power of Z ; p2=parallel planes, p3=rotation point and parallel planes a=real(p1), b=imag(p1) z=sin(a*.01745329251994)*real(pixel)+p2 c=cos(a*.01745329251994)*real(pixel)+flip(imag(pixel))+p3: z=(-z)^b+c |z| <= 16 ;SOURCE: 97msg.frm } MiraSinPar {; Peter Anders anders@physik.hu-berlin.de xo=real(p1), yo=imag(p1), a=real(pixel), b=imag(pixel): f=a*xo+(2-2*a)*sin(xo) x=b*yo+f f=a*x+(2-2*a)*sin(x) y=-xo+f z=x+y*(0,1) xo=x yo=y |fn1(z)|<real(p2) ;SOURCE: anders.frm } Mite (XAXIS) {; That mandel-thingy looks like mite, yes? Or a rabbit :). z = pixel: z1 = z*z+pixel z2 = z*z*z+(p1) z = z1+z2-(z1/z2) |z| <= 4 ;SOURCE: jute.frm } MixInv2waypro {; Jim Muth z=c=pixel: z=(-z)^p1+(p2*(-z)^p3)+c |z| <= 100 ;SOURCE: 98msg.frm } MixMan2waypro {; Jim Muth ; As posted in Fractal-Art, 5/10/97 z=c=pixel: z=z^p1+(p2*z^p3)+c |z| <= 100 ;SOURCE: 97msg.frm } MixMan3wayPro {; Jim Muth ; Replaced variable "e" with "ee" 5/05/99. G. Martin z=g=pixel, a=real(p1), b=imag(p1), c=real(p2) d=imag(p2), ee=real(p3), f=imag(p3): z=(a*z^b)+(c*z^d)+(ee*z^f)+g |z| <= 100 ;SOURCE: 97msg.frm } MixSqrProJulib {; Jim Muth ; As posted in Fractal-Art, 5/5/96 ; Replaced variable "e" with "ee" 5/05/99. G. Martin z=pixel, a=real(p1), b=imag(p1) c=real(p2), d=imag(p2), ee=p3+(d*pixel): z=(a*sqr(z))+(b*z^c)+ee |z| <= 100 ;SOURCE: 97msg.frm } MixSqrProJulib_2 {; Jim Muth ; Replaced variable "e" with "ee" 5/05/99. G. Martin z=pixel, a=real(p1), b=imag(p1) c=real(p2), d=imag(p2), ee=p3+(d*pixel): z=(a*sqr(z))+(b*z^c)+ee |z| <= 100 ;SOURCE: 97msg.frm } mixup { z=fn1(pixel): z=sqr(z)+fn2(pixel) |z|<= 4 ;SOURCE: test.frm } MixUpJ {; (c) Jay Hill, 1998 ; make sure p1 <> p2 and w <> 0 u=p1, v=p2, w=.5, x=v-u c=p3 ; Julia parameter z=pixel ; critical z=(-u/v/w)^(1/x) : z=z^u + w*z^v + c |z| <= 1000 ;SOURCE: 98msg.frm } MixUpJ2 {; (c) Jay Hill, 1998 ; make sure p1 <> p2 and p3 <> 0 u=p1, v=p2, w=p3, x=v-u c=pixel/w z=(-u/v/w)^(1/x) : z=z^u + w*z^v + c |z| <= 1000 ;SOURCE: Muth's FOTD 2005-10-15 } MJ_Maxi(XAXIS_NOIMAG) {; an automatic Mix ; staggering from M- to J-Set z = a = pixel b = p1 bailout = |p1| + 8: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = v ELSE z = u ENDIF |z|<bailout ;SOURCE: 97msg.frm } MJ_Mini(XAXIS_NOIMAG) {; an automatic Mix ; staggering from M- to J-Set z = a = pixel b = p1 bailout = |p1| + 8: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = u ELSE z = v ENDIF |z|<bailout ;SOURCE: 97msg.frm } MJM-PHC004 { z=0, c=pixel newpixel=pixel, iter=0 reduction=real(p1) + (real(p1)==0) nextzoom=iterspace=(p3>0)*p3 + (p3<=0)*256 rotation=pi*flip(imag(p1))/180 compt=0, limit = 100, bailout = 4 p = (-0.743380900000982,-0.131850030300002): test = (iter == nextzoom) test1 = (compt<limit) nextzoom = nextzoom + test*iterspace newpixel = newpixel*(1-test) + test*reduction*(newpixel-p2)*exp(rotation) z = z*(1 - test) c = (c*(1 - test) + test*newpixel) * whitesq + (c*test1+p*(1-test1)) * (whitesq == 0) z = z*z + c iter = iter + 1 compt = compt+1 |z| <= 16 ;SOURCE: nm_mj.frm } MJM-PHC01 { z = c = pixel compt = 0, limit = real(p1), bailout = 4 c1 = (0.34396372130558980 , 0.05608272738673762) c2 = (-0.72141758920523890 , 0.25918045895127010) delta = c2-c1, b = c+delta: p = (-0.743380900000982,-0.131850030300002) test1 = (compt<limit), test2 = (compt!=limit) z = z * fn1(test1) c = (b - delta * test1) * (whitesq == 0)\ + (c*test1+p*(1-test1)) * whitesq z = z*z+c compt = compt+1 |z| <= bailout ;SOURCE: mjm-phc.frm } MJM-PHC02 { z=0, c=pixel newpixel=pixel, iter=0 reduction=real(p1) + (real(p1)==0) nextzoom=iterspace=(p3>0)*p3 + (p3<=0)*256 rotation=pi*flip(imag(p1))/180 compt=0, limit = 100, bailout = 4 p = (-0.743380900000982,-0.131850030300002): test = (iter == nextzoom) test1 = (compt<limit) nextzoom = nextzoom + test*iterspace newpixel = newpixel*(1-test) \ + test*reduction*(newpixel-p2)*exp(rotation) z = z*(1 - test) c = (c*(1 - test) + test*newpixel) * whitesq\ + (c*test1+p*(1-test1)) * (whitesq == 0) z = z*z + c iter = iter + 1 compt = compt+1 |z| <= 16 ;SOURCE: mjm-phc.frm } MJM-PHC03 { z=0, c=pixel newpixel=pixel, iter=0 reduction=real(p1) + (real(p1)==0) nextzoom=iterspace=(p3>0)*p3 + (p3<=0)*256 rotation=pi*flip(imag(p1))/180 compt=0, limit = 100, bailout = 4 p = (-0.743380900000982,-0.131850030300002): test = (iter == nextzoom) test1 = (compt<limit) nextzoom = nextzoom + test*iterspace newpixel = fn1(newpixel)*(1-test)\ + test*reduction*(fn2(newpixel)-p2)*exp(rotation) z = z*(1 - test) c = (c*(1 - test) + test*newpixel) * (whitesq == 0)\ + (c*test1+p*(1-test1)) * whitesq z = z*z + c iter = iter + 1 compt = compt+1 |z| <= 16 ;SOURCE: mjm-phc.frm } MJM-PHC04 { z=0, c=pixel newpixel=pixel, iter=0 reduction=real(p1) + (real(p1)==0) nextzoom=iterspace=(p3>0)*p3 + (p3<=0)*256 rotation=pi*flip(imag(p1))/180 compt=0, limit = 100, bailout = 4 p = (-0.743380900000982,-0.131850030300002): test = (iter == nextzoom) test1 = (compt<limit) nextzoom = nextzoom + test*sqrt(iterspace) newpixel = newpixel*(1-test)\ + test*reduction*(newpixel-p2)*exp(rotation) z = z*(1 - test) c = (c*(1 - test) + test*newpixel) * (whitesq == 0)\ + (c*test1+p*(1-test1)) * whitesq z = z*z + c iter = iter + 1 compt = compt+1 |z| <= 16 ;SOURCE: mjm-phc.frm } MJM-PHC05 { z=0, c=pixel newpixel=pixel, iter=0 reduction=real(p1) + (real(p1)==0) nextzoom=iterspace=(p3>0)*p3 + (p3<=0)*256 rotation=pi*flip(imag(p1))/180 compt=0, limit = 100, bailout = 4 p = (-0.743380900000982,-0.131850030300002): test = (iter == nextzoom) test1 = (compt<limit) nextzoom = nextzoom + test*iterspace newpixel = newpixel*(1-test)\ + test*flip(reduction)*(newpixel-p2)*exp(rotation) z = z*(1 - test) c = (c*(1 - test) + test*newpixel) * (whitesq == 0)\ + (c*test1+p*(1-test1)) * whitesq z = z*z + c iter = iter + 1 compt = compt+1 |z| <= 16 ;SOURCE: mjm-phc.frm } MJM-PHC06 { z=0, c=pixel newpixel=pixel, iter=0 reduction=real(p1) + fn1((real(p1)==0)) nextzoom=iterspace=(p3>0)*p3 + (p3<=0)*256 rotation=pi*flip(imag(p1))/180 compt=0, limit = 100, bailout = 4 p = (-0.743380900000982,-0.131850030300002): test = fn3(iter == nextzoom) test1 = fn4(compt<limit) nextzoom = nextzoom + test*iterspace newpixel = newpixel*(1-test)\ + test*flip(reduction)*fn2(newpixel-p2)*exp(rotation) z = z*(1 - test) c = (c*(1 - test) + test*newpixel) * (whitesq == 0)\ + (c*test1+p*(1-test1)) * whitesq z = z*z + c iter = iter + 1 compt = compt+1 |z| <= 16 ;SOURCE: mjm-phc.frm } MJM-PHC07 { z=0, c=pixel newpixel=pixel, iter=0 reduction=real(p1) + (real(p1)==0) nextzoom=iterspace=(p3>0)*p3 + (p3<=0)*256 rotation=pi*flip(imag(p1))/180 compt=0, limit = 100, bailout = 4 p = fn1(-0.743380900000982,-0.131850030300002)\ ^fn2(-0.743380900000982,-0.131850030300002): test = (iter == nextzoom) test1 = (compt<limit) nextzoom = nextzoom + test*iterspace newpixel = newpixel*(1-test)\ + test*flip(reduction)*(newpixel-p2)*exp(rotation) z = z*(1 - test) c = (c*(1 - test) + test*newpixel) * whitesq\ + (c*test1+p*(1-test1)) * (whitesq == 0) z = z*z + c iter = iter + 1 compt = compt+1 |z| <= 16 ;SOURCE: mjm-phc.frm } MJM-PHC08 { z=0, c=pixel newpixel=pixel, iter=0 reduction=real(p1) + (real(p1)==0) nextzoom=iterspace=(p3>0)*p3 + (p3<=0)*256 rotation=pi*flip(imag(p1))/180 compt=0, limit = 100, bailout = 4 p = fn1(p2): test = (iter == nextzoom) test1 = (compt<limit) nextzoom = nextzoom + test*iterspace newpixel = newpixel*(1-test)\ + test*flip(reduction)*(newpixel-p2)*exp(rotation) z = z*(1 - test) c = (c*(1 - test) + test*newpixel) * whitesq\ + (c*test1+p*(1-test1)) * (whitesq == 0) z = z*z + c iter = iter + 1 compt = compt+1 |z| <= 16 ;SOURCE: mjm-phc.frm } MNDLPIER (XAXIS) { z=pixel-1: z=sqr(z) +log(pixel) |z|<=4 ;SOURCE: newform.frm } Mnemonics { z = c = pixel: r = fn1(z) + p1 q = atan(cos(z))/tan(sin(z)) + c z = r * fn2(1/z * q) |z| < 4 ;SOURCE: astral.frm } moc { z=0, c=pixel: z=sqr(z)+c c=c+p1/c |z| <= 4 ;SOURCE: fractint.frm } Mod-August4 {; Modified Sylvie Gallet frm, Dec 1997 ; Modified by Brian E. Jones ; Coloring algorithm by Scott Burns ; Use decomp = 256 and periodicity = 0 z1 = pixel, iter = 0, sq2 = sqrt(2) a = real(p1)*(0,0.0245436) ; real(p1) * 2i pi / 256 mz = abs(cabs(z1)-sq2) : IF (mz > 0.1) z2 = fn1(z1/z1)*fn2(z1) z1 = (3*z2*z2 - 4) / (4*z1*z2) mz = abs(cabs(z1)-sq2) cont = 1 iter = iter + 1 ELSE IF (iter < 13) z = exp((iter + 0.001 + 9.99*mz)*a) ELSE z = exp((13 + (iter-13)/18)*a) ENDIF cont = 0 ENDIF cont ;SOURCE: 97msg.frm } Modified_a Gallet-3-11 {; Sylvie Gallet [101324,3444], 1996 z=fn1(pixel^p1/p2+p2*pixel/fn2(p1^pixel)), p=p2/p1: z = z*p (z+p) <= p1 ;SOURCE: bej's2.frm } Moe {; Mutation of 'Zexpe'. ; Original formula by Lee Skinner [75450,3631] ; Modified for if..else logic 3/19/97 by Sylvie Gallet ; For 'Zexpe', set FN1 & FN2 = IDENT and P1 = default ; real(p1) = Bailout (default 100) s = exp(1.,0.), z = pixel, c = fn1(pixel) ; The next line sets test=100 if real(p1)<=0, else test=real(p1) IF (real(p1) <= 0) test = 100 ELSE test = real(p1) ENDIF : z = fn2(z)^s + c |z| <= test ;SOURCE: fract196.frm } MOne_Maxi {; generalized Minimax-Set (p1<>0!) ; normal M-Set for p1=1 ; p1 = -1 gives Mpm_Maxi z = a = pixel b = p1/cabs(p1) * pixel IF(p3==0) bailout=8 ELSE bailout = |p3| ENDIF: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = v ELSE z = u ENDIF |z|<=bailout ;SOURCE: 97msg.frm } MOne_Mini {; generalized Minimax-Set (p1<>0!) ; normal M-Set for p1=1 ; p1 = -1 gives Mpm_Mini z = a = pixel b = p1/cabs(p1) * pixel IF(p3==0) bailout=8 ELSE bailout = |p3| ENDIF: qz = sqr(z) u = qz + a v = qz + b IF(|u|<|v|) z = u ELSE z = v ENDIF |z|<=bailout ;SOURCE: 97msg.frm } mongo-01 { z = c = pixel: z = p1 * fn1(z^z + c) + c/z |z| <= p2 ;SOURCE: mongo.frm } mongo-02 {; TRY P1 REAL = -1, P2 = 5, FN1 = SQR, FN2 = RECIP z = 0, c = pixel: z = fn2(fn1(z) + c) + (p1 * z) |z| <= p2 ;SOURCE: mongo.frm } mongo-03 { z = c = pixel: a = (abs(z) > p1) * (fn1(z) + c) b = (abs(z) <= p1) * (fn2(z) + c) z = a + b |z| <= p2 ;SOURCE: mongo.frm } mongo-04 { z = c = pixel, test = p1/p2: a = fn1(z) b = (|z| > test) * (a - c) d = (|z| <= test) * (a + c) z = b + d |z| <= p1 ;SOURCE: mongo.frm } mongo-05 { z = pixel, c = fn1(pixel): a = fn2(z) b = (|z| >= p1) * (a - c) d = (|z| < p1) * (a + c) z = a + b + d |z| <= p2 ;SOURCE: mongo.frm } mongo-06 {; Replaced variable "e" with "ee" 5/05/99. G. Martin z = c = pixel, d = fn1(pixel): a = fn2(z) b = (z <= p1) * (a + c + d) ee = (z > p1) * (a + c - d) z = z + b + ee |z| <= p2 ;SOURCE: mongo.frm } mongo-07 { z = v = pixel: oldz = z z = fn1(z)^p1 + v v = oldz |z| <= p2 ;SOURCE: mongo.frm } mongo-08 {; Replaced variable "e" with "ee" 5/05/99. G. Martin z = v = pixel: a = fn1(z) b = (z <= p1) * (a + v) ee = (z > p1) * (a - v) v = z z = b + ee |z| <= p2 ;SOURCE: mongo.frm } mongo-09 {; Replaced variable "e" with "ee" 5/05/99. G. Martin z = v = pixel: a = fn1(z) b = (a <= p1) * (a + v) ee = (a > p1) * fn2(a) v = z z = b + ee |z| <= p2 ;SOURCE: mongo.frm } mongo-10 {; Replaced variable "e" with "ee" 5/05/99. G. Martin z = y = x = pixel: a = fn1(z) b = (a <= y) * ((a * p1) + y) ee = (a > y) * ((a * p1) + x) x = y y = z z = b + ee |z| <= p2 ;SOURCE: mongo.frm } mongo-11 { z = y = x = pixel: a = (|y| <= p1) * fn1(y) b = (|x| <= p1) * fn2(x) x = y y = z z = fn3(z) + a + b |z| <= p2 ;SOURCE: mongo.frm } mongo-12 { z = pixel, c = (fn1(pixel) * p1): x = abs(real(z)) y = abs(imag(z)) a = (x <= y) * (fn2(z) + y + c) b = (x > y) * (fn2(z) + x + c) z = a + b |z| <= p2 ;SOURCE: mongo.frm } mongo-13 { z = pixel: v = fn1(z) x = (z*v) y = (z/v) a = (|x| <= |y|) * ((z + y) * p1) b = (|x| > |y|) * ((z + x) * p1) z = fn2((a + b) * v) + v |z| <= p2 ;SOURCE: mongo.frm } monkey (XAXIS) {; rlbagula z = Pixel: z = 1/(z*sin(1/z)+pixel) z = Sqr(z) LastSqr <= 4 ; Use LastSqr instead of recalculating ;SOURCE: rbagula.frm } monkey2 (XAXIS) {; rlbagula z = Pixel: z = 1/(sqr(z)*sin(1/sqr(z))+pixel) LastSqr <= 16 ; Use LastSqr instead of recalculating ;SOURCE: rbagula.frm } monkey2i (XAXIS) {; rlbagula z = Pixel: z = (sqr(z)*sin(1/sqr(z))+pixel) LastSqr <= 16 ; Use LastSqr instead of recalculating ;SOURCE: rbagula.frm } monkey3i (XAXIS) {; rlbagula z = Pixel: z = (z*sqr(z)*sin(1/(z*sqr(z)))+pixel) LastSqr <= 16 ; Use LastSqr instead of recalculating ;SOURCE: rbagula.frm } monkey4i (XAXIS) {; rlbagula z = Pixel: z = (sqr(sqr(z))*sin(1/sqr(sqr(z)))+pixel) LastSqr <= 16 ; Use LastSqr instead of recalculating ;SOURCE: rbagula.frm } Monkey_Type_1 { z = Pixel: z = sin(z*z/(z+ (2.34,.2)) + asin(z) - flip(log(z))) |z| <= 4 ;SOURCE: forummsg.frm } Monkey_type_2 { z = Pixel: z = sin(z*z/(z+ (2.34,.2)) + asin(z) - flip(log(z))) + Pixel |z| <= 4 ;SOURCE: forummsg.frm } monument {; Giuseppe Zito z = pixel c0 = -0.97078 c5 = 0.196811 : x = real(z), y = imag(z) s0 =c0 s0 = s0 *x s1 = x s0 = s0 *s1 s0 = s0 +c5 s0 = s0 /y newx = s0 s0 = y s0 = s0 -y s0 = s0 *x s0 = s0 *x s0 = s0 -x newy = s0 z = newx + flip(newy) newx < 4 && newx > -4 && newy < 4 && newy > -4 ;SOURCE: zg.frm } Moo {; Requires Periodicity=0 ; significant speedup of MOO, artists take note!!! ; Revised 6/8/96 for orgform, speedup using halfe suggested ; by Tim Wegner halfe = e*(-.5), z = pixel: z = z + p1 r = tan(1/z) + pixel z = fn1(z)*r^halfe ; was z = fn1(z)/sqrt(r)^e |z| < 4 ;SOURCE: mad_cow.frm } Moo_2 {; requires periodicity=0 ; revision 6/10/96 by G. Martin for Orgform of a Vincent Presogna ; formula of the same name ; speedup of original, substituting quartere for e/4 and ; r^quartere for sqrt(r)^(e/2) ; speedup technique pointed out by Tim Wegner z = pixel, quartere = e*(-.25): z = z + p1 r = tan(1/z) * pixel z = fn1(z)*r^quartere ; was fn1(z)/sqrt(r)^(e/2) |z| < 4 ; SOURCE: mad_cow.frm } Moo_3 {; requires periodicity=0 z = pixel: z = z + p1 r = tan(1/z) * pixel z = fn1(z)/sqrt(r) |z| < 4 ;SOURCE: mad_cow.frm } Moo_4 { z = pixel: z = z + p1 r = tan(1/z) + pixel z = fn1(z)/sqrt(r) |z| < 4 ;SOURCE: mad_cow.frm } Moo_PHC {; by Vincent Damion Presogna, Oct. 18, 1996 z = pixel halfe = e*(-0.5) quartere = e*(-.25): z = z + p1 y = tan(1/z) r = y + pixel q = y * pixel z = fn2(z)*r^halfe*(whitesq == 0) + fn1(z)*q^quartere*(whitesq) |z| <= 4 ;SOURCE: 96msg.frm } Mooey { ; revision 6/10/96 by G. Martin for Orgform of a Vincent Presogna ; formula of the same name ; speedup of original, substituting sroote for sqrt(e) and ; r for /sqrt(1/r)^2 ; speedup technique pointed out by Tim Wegner z = pixel, sroote = sqrt(e): r = tan(1/z)^sroote + pixel z = fn1(z) * r ; was fn1(z)/sqrt(1/r)^2 |z| < 4 ; SOURCE: mad_cow.frm } Moonworld {; inspired by Heron's formula ; (c) 1997 Bernd Lehnhoff ; use floating point and periodicity=no! ; p1 is the radicand ; p2 is a perturbation v = pixel IF(p2==0) p2=0.5 ENDIF a = log(|p2|)-12 c = sqr(p1): u = v v = (u + c/u)/2 + p2 z = v - u log(|z|) >= a ;SOURCE: 97msg.frm } Moonworld_3 {; Generalized version of Moonworld ; (c) 1997 Bernd Lehnhoff ; use floating point and periodicity=no! ; p1 is the radicand ; p2 is the perturbation IF(p2==0) p2=0.5 ENDIF v = pixel a = log(|p2|)-12: u = v v = u-u/3*(1-(p1/u)^3)+p2 z = v - u log(|z|) >= a ;SOURCE: 97msg.frm } Moonworld_general {; Generalized version of Moonworld ; (c) 1997 Bernd Lehnhoff ; use floating point and periodicity=no! ; p1 is the radicand ; p2 is the perturbation ; p3 is the degree IF(p2==0) p2=0.5 ENDIF v = pixel a = log(|p2|)-12: u = v v = u-u/p3*(1-(p1/u)^p3)+p2 z = v - u log(|z|) >= a ;SOURCE: 97msg.frm } MORPHS {; Ray Girvan ; Newton variant giving biomorphs ; z -> sin(z) before Newton iteration ; use floating point, periodicity=no ; try p1=0.1, p2=3 for bees ; p1=0.1, p2=6 for crabs z=pixel: z1=sin(z)-p1 z2=z1^p2-1 z3=p2*(z1^(p2-1)) z=z-(z2/z3) |z2| >= 0.00001 ;SOURCE: 97msg.frm } Mosaic {; Jim M, thanks to someone unknown ; p1=Mandelbrot set coordinates z=c=p1+.05*(fn1(fn2(real(pixel)))+flip(fn3(fn4(imag(pixel))))): z=sqr(z)+c |z| <= 100 ;SOURCE: 97msg.frm } Moth (XAXIS_NOPARM) { ; Edited for Fractint v. 20 by George Martin 10/98 z=p1, x=1: z=sqr(z)+pixel z=exp(z)+pixel z=log(z)+pixel x=x+1 |z|<=4 ;SOURCE: choice.frm } MothC (XAXIS_NOPARM) { ; Edited for Fractint v. 20 by George Martin 10/98 z=p1, x=1: IF (x<10) z=sqr(z)+pixel ELSEIF (x<20) z=exp(z)+pixel ELSE z=log(z)+pixel ENDIF x=x+1 |z|<=4 ;SOURCE: choice.frm } Mothra (XAXIS) {; Ron Lewen, 76376,2567 ; Remember Mothra, the giant Japanese-eating moth? ; Well... here he (she?) is as a fractal! z=pixel: a=z^5 + z^3 + z + pixel b=z^4 + z^2 + pixel z=b^2/a |real(z)| <= 100 || |imag(z)| <= 100 ;SOURCE: fractint.frm } moz { z=0, c=pixel: z=sqr(z)+c c=c+p1/z |z| <= 4 ;SOURCE: explode.frm } Mpm_Maxi(XYAXIS) {; an automatic Mix z = a = pixel IF(p1==0) bailout=8 ELSE bailout = |p1| ENDIF: qz = sqr(z) u = qz + a v = qz - a IF(|u|<|v|) z = v ELSE z = u ENDIF |z|<bailout ;SOURCE: 97msg.frm } Mpm_Mini(XYAXIS) {; an automatic Mix z = a = pixel IF(p1==0) bailout=8 ELSE bailout = |p1| ENDIF: qz = sqr(z) u = qz + a v = qz - a IF(|u|<|v|) z = u ELSE z = v ENDIF |z|<bailout ;SOURCE: 97msg.frm } mrosa {; Giuseppe Zito z = pixel c0 = -0.90967202 c2 = -0.79515898 d3 = -0.99741298 d4 = -0.667045 d7 = -0.309879 : x = real(z), y = imag(z) s0 =c0 s0 = s0 -c2 s0 = s0 -y s0 = s0 +x newx = s0 s0 = y s0 = s0 -x s0 = s0 *x s1 =d3 s1 = s1 *d4 s0 = s0 +s1 s0 = s0 +d7 s0 = s0 +x newy = s0 z = newx + flip(newy) newx < 4 && newx > -4 && newy < 4 && newy > -4 ;SOURCE: zg.frm } mt_990128f {; Mark Townsend, 28-01-99 ; real p1 coloring speed of points captured by the Y axis ; imag p1 coloring speed of points captured by the X axis ; real p2 bailout point for orbits nearing the Y axis ; imag p2 bailout point for orbits nearing the X axis ; p3 Julia coordinates ; fn1 function for the fractal formula ('ident' for Julia) ; fn2 function for coloring points captured by the Y axis ; fn3 function for coloring points captured by the X axis ; fn4 function for the outside coloring ; use decomp=256 ; ; This is an implementation of Pickover's 'epsilon cross' ; method on a generalised Julia fractal. The user can set ; how near the orbit has to get to the axes before bailing ; out. The larger the values given to p2 the wider the ; 'stalks'. The values should be positive or 0 to turn the ; stalks off. Points within the stalks are coloured by the ; angle of z at bailout, messed up by a function. The outside ; is coloured by the angle of z on it's closest approach to the ; origin, again through a function. ; ; *********************************** z = pixel, c = p3, iter = 1, s = 1e9: ; *********************************** z = fn1(sqr(z)) + c ; find the closest z to to the origin IF (|z| < |s|) s = z ENDIF IF (abs(real(z)) < real(p2)) ; caught by Y axis z = fn2(z)^real(p1) iter = 0 ELSEIF (abs(imag(z)) < imag(p2)) ; caught by X axis z = fn3(z)^imag(p1) iter = 0 ELSEIF (|z| > 4) z = fn4(s) iter = 0 ENDIF iter > 0 ;SOURCE: 99msg.frm } MTet (XAXIS) {; Mandelbrot form 1 of the Tetration formula --Lee Skinner z = pixel: z = (pixel ^ z) + pixel |z| <= (P1 + 3) ;SOURCE: fractint.frm } MtNwt5_1/fn12 { z = 1/fn1(p1 * pixel) + 1/fn2(p2 * pixel), Root = 1: z = (4 * z^5 + Root) / (5 * z^4) 0.001 <= |z^5 - Root| ;SOURCE: crazynwt.frm } MtNwt5_fn12 { z = fn1(p1 * pixel) + fn2(p2 * pixel), Root = 1: z = (4 * z^5 + Root) / (5 * z^4) .001 <= |z^5 - Root| ;SOURCE: crazynwt.frm } MtNwtfn1[fn2] { z = fn1(fn2(p2*pixel)), Root = 1 : z = ((p1-1) * z^p1 + Root) / (p1 * z^(p1-1)) .001 <= |z^p1 - Root| ;SOURCE: crazynwt.frm } mtofn { z=pixel: power = fn2(z) z = z^power + pixel |z| < p2 ;SOURCE: fractals.frm } mult1-5-XY-ZW {; draws all 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=(real(p1)+10^(-100))*.01745329251994 b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=z^1.5+c |z| <= 36 ;SOURCE: 98msg.frm } mult1-5-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=z^1.5+c |z| <= 36 ;SOURCE: 98msg.frm } mult105-XY-ZW {; draws all 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=(-z)^1.05+c |z| <= 36 ;SOURCE: 98msg.frm } mult2-003-XY-ZW {; draws all 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=(real(p1)+10^(-100))*.01745329251994 b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=z^2.003+c |z| <= 36 ;SOURCE: 98msg.frm } mult2-003-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=z^2.003+c |z| <= 36 ;SOURCE: 98msg.frm } mult2-5-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=z^2.5+c |z| <= 36 ;SOURCE: 98msg.frm } Multbrot {; Tom Schumm ; Attempt to change the shape of the escape boundry z = Pixel, z = Sqr(z): ; Just like mandel z = z + Pixel z = Sqr(z) imag(z)*real(z) <= 4 ; Different escape boundry ;SOURCE: phong.frm } MultdBail {;p1 is dist switch, p2 is count switch z = c = pixel, x=0, m=1: x=x+1, t = z*z+c, d=|z|/4, do=1-d g = (d<=p1)* (x<=p2)* (1.25), h=(d>p1)* (x<=p2)* (.9) i = (d<=p1)* (x>p2)* (1.1), j=(d>p1)* (x>p2)* (1) m = (g+h+i+j)*m z = m*t d <= 4 ;SOURCE: ron1.frm } multesc4-XY-ZW {; draws 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(z)+c |z| < 4 ;SOURCE: 99msg.frm } multi1-5-XY-ZW {; draws all 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=z^1.5+c |z| <= 36 ;SOURCE: 98msg.frm } multi20031 {; formula draws many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=((real(p1))+(.000000000000000000001))*.01745329251994 b=((imag(p1))+(.000000000000000000001))*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=z^2.003+c |z| <= 36 ;SOURCE: 98msg.frm } multi20031a {; draws all six planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=((real(p1))+(.000000000000000000001))*.01745329251994 b=((imag(p1))+(.000000000000000000001))*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=z^2.003+c |z| <= 36 ;SOURCE: 0from_ml.frm } multi20032 {; Jim Muth this is the formula ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=z^2.003+c |z| <= 100 ;SOURCE: 98msg.frm } Multia (ORIGIN) {; Tom Schumm ; Attempt to change the shape of the escape boundry z = Pixel, z = Sqr(z): ; Just like julia z = z + p1 z = Sqr(z) imag(z)*real(z) <= 4 ; Different escape boundry ;SOURCE: phong2.frm } multicub-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=z*z*z+c |z| <= 36 ;SOURCE: 98msg.frm } multifract1 {; Ron Barnett, January 1999 ; Use decomp = 256 or outside = atan ; Use imag(p3) to change the color spread zc = z = c = pixel IF ((real(p1)) == 0 && (imag(p1) == 0)) p1 = (0,-0.5) ENDIF IF ((real(p2)) == 0 && (imag(p2) == 0)) p2 = 1 ENDIF IF (real(p3) == 0) p3 = p3 + (10000,0) ENDIF IF (imag(p3) == 0) p3 = p3 + (0,10) ENDIF choice = iterexp = 0: choice = (choice == 0) IF (choice == 0) zc = p2*(zc*zc + c) iterexp = iterexp + exp(-cabs(zc)) ELSE z1 = exp(zc) z2 = sin(zc) + z1 - 1 zc = zc - p1*z2/(cos(zc) + z1) ENDIF IF (|zc| > real(p3)) smooth = iterexp*imag(p3)*pi/128 ang = cos(smooth)+flip(sin(smooth)) z = 256*ang ENDIF |zc| <= real(p3) ;SOURCE: 99msg.frm } multigator2 {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Edited for Fractint v. 20 by George Martin, 10/98 ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=(.5*(z^(-4)))+(-2*(z^(-2)))+c |z| <= 100 ;SOURCE: 97msg.frm } multirot-pm21 {; Jim Muth, best=ifif, fiif, fifi, iffi a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*fn3(real(pixel))+cos(a)*fn4(imag(pixel))+p3: z=(.1*(sqr(z)))+(10*(z^(-2)))+c |z| <= 100 ;SOURCE: 97msg.frm } multirot-XY-ZW {; draws all 6 planes and many rotations NEW version ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(z)+c |z| <= 36 ;SOURCE: 98msg.frm } multirot-XY-ZWa {; draws all 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(z)+c |z| <= 36 ;SOURCE: 0from_ml.frm } multirot-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=sqr(z)+c |z| <= 36 ;SOURCE: 98msg.frm } multirot03-XY-ZW {; draws 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=z*z*z+c |z| <= 36 ;SOURCE: 99msg.frm } multirot03-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=z*z*z+c |z| <= 36 ;SOURCE: 99msg.frm } multirot04-XY-ZW {; draws 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(sqr(z))+c |z| <= 36 ;SOURCE: 98msg.frm } multirot04-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=sqr(sqr(z))+c |z| <= 36 ;SOURCE: 98msg.frm } multirot05-XY-ZW {; draws 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=z*(sqr(sqr(z)))+c |z| <= 36 ;SOURCE: 99msg.frm } multirot05-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=z*(sqr(sqr(z)))+c |z| <= 36 ;SOURCE: 98msg.frm } multirot06-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect ; Replaced variable "e" with "ee" 5/05/99. G. Martin ee=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=ee*imag(pixel)+p3: z=sqr(z)*sqr(sqr(z))+c |z| <= 36 ;SOURCE: 98msg.frm } multirot07-XY-ZW {; draws 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=z*(sqr(z)*sqr(sqr(z)))+c |z| <= 36 ;SOURCE: 98msg.frm } multirot16-XY-ZW {; draws 6 planes and rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(sqr(sqr(sqr(z))))+c |z| <= 36 ;SOURCE: 99msg.frm } multmin1-2-XY-ZW {; draws all 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real((p1)+.000000000000000000000000000001)*.01745329251994 b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=(-z)^1.2+c |z| <= 36 ;SOURCE: 98msg.frm } multmin1-5-XY-ZW {; draws 6 planes and many rotations ; when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ; when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=(real(p1)+10^(-100))*.01745329251994 b=imag(p1)*.01745329251994 z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2 c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=(-z)^1.5+c |z| <= 36 ;SOURCE: 99msg.frm } multmin3-5-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))) f=exp(flip(imag(p1*.01745329251994))) z=f*real(pixel)+p2, c=e*imag(pixel)+p3: z=(-z)^3.5+c |z| < 36 ;SOURCE: 99msg.frm } murano {; Giuseppe Zito z = pixel c2 = 0.68162298 c12 = -0.093601 c16 = -0.26411101 c26 = 0.004199 c29 = 0.251564 c31 = -0.80334002 d1 = -0.95945197 d5 = -0.458745 d12 = -1.08000004 d15 = -0.27162501 d19 = -0.562644 d20 = 0.646236 : x = real(z), y = imag(z) s0 = y s0 = s0 /c2 s1 = x s0 = s0 +s1 s0 = s0 *y s0 = s0 +x s1 =c12 s1 = s1 /x s1 = s1 /c16 s1 = s1 *x s0 = s0 *s1 s0 = s0 +y s0 = s0 -y s0 = s0 +x s0 = s0 *c26 s0 = s0 /x s0 = s0 *x s0 = s0 -c29 s0 = s0 /c31 s0 = s0 -y newx = s0 s0 = y s0 = s0 /d1 s0 = s0 +y s0 = s0 *y s0 = s0 -d5 s0 = s0 -y s0 = s0 +y s1 =d12 s1 = s1 *x s1 = s1 /x s1 = s1 -d15 s0 = s0 *s1 s0 = s0 /x s0 = s0 -d19