170mm x 244mm Collerton c10. tex V3-11/21/2014 5:28 P. M. Page 242 242 CH10 GEOMETRIC VISUAL HALLUCINATIONS (a) (b) Figure 10. 21 (a) Irregular stripes generated by simulating the Ermentrout-Cowan equations with only a local Mexican Hat connectivity, and no long-range connections. (b) Effects of cou-plingthisconnectivitypatterntoaplanarlatticeofhorizontalconnectionsbetweenhypercolumns. Lattice sites,indicated bythedots,represent iso-orientationpatches of oneunique preference. 2 1 0-1-2-3-2-1 0 1 2 3 Wavenu mber k (in units of 2 π/d0) (b)-3 -2-1 0 1 2 3 Cortical position x (in units of d0). 15. 1. 05 0-. 05-. 1 (a) Figure 10. 22 (a)Aone-dimensionallatticewithconnectionsthatweakenwithdistancebetween latticepoints,togetherwiththeprofileofaone-dimensional Mexican Hatconnectivityusedinthe Ermentrout-Cowan model. (b) The Fourier spectra of the profiles shown in (a). The dark grey curves represent thesuperpositionof the twoweighting functions. 10. 4. 3 Intrinsic ﬂuctuations We now consider the question of what triggers the hallucinations. The calculations we have carried out on the stability of the spatially homogeneous state of V1 indi-cate that when such a state loses stability to small fluctuations, it is usually the result of changes in the coupling parameters of the underlying circuitry, or by the