of an embryo along various directions from an original spherical state. A hallmark of each of these examples is that there is no input into the system, so the emergent patterns reflect amechanism of spontaneous symmetry breaking, onset by a perturbation of “some influences unspecified ”(Turing, 1952 ). In light of this, we ask, can the visual cortex self-generate the perception of hue? Spontaneous symmetry breaking and color hallucinations. To assess our model 's ability to self-organize in the absence of visual input, we set c= 0 and seek to establish the presence of a Turing mechanism marked by the following three features: 1. A system comprised of local excitation and long-range inhibition. 2. Spontaneous symmetry breaking in the absence of input within a region of a parameter space defined by the relevant bifurcation parameter(s). 3. The emergence of patterns that are bounded by the system 's nonlinearities. As noted above, requiring DX<DYin Equation 34 sets up the diffusion-driven activator-inhibitor dynamics governing the evolution of the morphogen concentration across the ring of cells. With these assumptions, Turing 's reaction-diffusion equations bear a strong resem-blance to our one-population generalization of the excitatory and inhibitory color cell dynam-ics in the absence of LGN input: τ0daθ;tð Þ dt¼-aθ;tð Þ þ g Zπ-πJ0þ J1cosθ-θ0ð Þ ð Þ aθ0;tð Þ dθ0/C20/C21 ; (36) where the local excitation and long-range inhibition are incorporated in the anisotropic inter-action term J1cos(θ-θ0), and the reaction terms a X(θ,t),b Y(θ,t),c X(θ,t), and d Y(θ,t) find their neural analogue in the term-a(θ,t). Importantly, the notions of “local ”and“long-range ” here describe interactions in the DKL space, and not in the physical cortical space correlate to Turing 's ring of tissue. Accordingly, we treat J1as the Turing bifurcation parameter and look for spontaneous color tuning beyond a bifurcation point J1=JT 1. Additionally, we observe that the onset of pattern formation is determined by a critical value of T, so that the relevant parameter space for our exploration is ( J1,T)(Figure 14 ). This analysis is summarized in Figure 15. Figure 14. The onset of color hallucinations in the ( J1,T) parameter space. The model generates spontaneous hue tuning curves beyond J1=JT 1≡1 πβand below T=0. Network Neuroscience 701Pattern forming mechanisms of color vision Downloaded from http://direct. mit. edu/netn/article-pdf/7/2/679/2118501/netn_a_00294. pdf by guest on 09 August 2024 