Billock, Cunningham & Tsou (2008) 10 APPROVED FOR PUBLIC RELEASEComparison to Related Studies: Dynamic Fractals So far we have discussed only perception of static fractals. But camouflaged images may move against their backgrounds and camouflage may be dynamic in other ways. In general, the effect of motion on such fractals is described by f t= v*f s (where v is velocity and f t is temporal frequency). Thus, if the spatial spectrum is a 1/f distribution, then for simple movement the temporal frequency distribution is a linear transform of spatial frequency, which is no more interesting than the viewing distance condition. There are however more interesting dynamic manipulations of fractals that are worth study. For example, it is possible to extend our study of discrimination to spatiotemporal fractals-fractals whose individual pixel intensities vary over time in a manner described by fractional Brownian motion. Such images have Fourier amplitude spectra of A(ft,fs) = kf tĮfsȕ Eq. 2 In general, as Į becomes larger, the motion of the texture becomes more coherent and can be used to mimic various biological motions (Billock et al., 2001a). Figure 6 shows the human perceptual discrimination space for spatiotemporal fractals (dynamic textures). Figure 6. Discrimination contours for spatiotemporal fractal textures (Eq. 2) using the same observers in Figures 3 and 4. The contours are estimated using JNDs for discrimination in four directions in the perceptual space and are fit using simple quarter-circles of no theoretical significance.