170mm x 244mm Collerton c10. tex V3-11/21/2014 5:28 P. M. Page 226 226 CH10 GEOMETRIC VISUAL HALLUCINATIONS Figure 10. 8 Funnel and spiral hallucinations in retinal and cortical coordinates. Source: Redrawn from Bressloff etal. (2001). periodic blob-like patterns, and the realization that the Turing mechanism for the development of stripes or spot patterns in animal coat markings (Turing, 1952) had a neural analogue. The Turing mechanism is implemented in terms of two diffusion-coupledchemicalreactions. Thefirstreactionisautocatalyticandinvolves a large molecule with a small diffusion constant; the second is autoinhibitory and involves a small molecule with a large diffusion constant. The equations take the form𝜕 𝜕tu(x,t)=-bu+∇2u+f(u,𝑣) 𝜕 𝜕t𝑣(x,t)=-𝑣+D∇2𝑣+g(u,𝑣) (10. 4) whereuand𝑣are the concentrations of the large and small molecules, fandgare nonlinearfunctionsof uand𝑣,implyingthatthereactionsinvolvebinaryorternary combinationsofthemolecules, bisthedecayconstantofthe ureaction,and Disthe diffusionconstantofthe 𝑣reaction. Thediffusionconstantofthe ureactionissetto one,asisthedecayconstantofthe 𝑣reaction. Turingwasabletoshowbycomputer simulation that a planar system of such coupled reactions could generate periodic