We observe that within the analytical regime, the system generates a stable homogeneous steady-state solution a∞(θ) = const ≥0 for all values of the parameters β,T,J0,a n d J1(Figure 15A-B). As such, from the closed-form linear steady-state solution ( Methods :Linear Solution ), we obtain a∞θð Þ ¼-βT 1-2πβJ0for T≤0 0 for T>0:8 < :(37) We further observe that beyond J1=1 πβ, a stable homogeneous steady-state solution remains at a∞(θ) = 0 for T≥0(Figure 15C ). However, at T= 0, this radial symmetry is broken, and the cortex generates spontaneous tuning curves with peak locations determined by the random initial conditions ( Figure 15D-F). Thus, the system bifurcates when J1=1 πβand T= 0, permitting the onset of color hallucinations in a region defined by these two values (Figure 14 ). Note that the unimodal tuning curves predict stationary, single-hued phosphenes. Extension to other CO blob networks would therefore indicate a hallucination comprised ofmultiple phosphenes of varied hues, each determined by the local cortical activity at hallu-cinatory onset. Bearing these predictions in mind, we point to a recent functional MRI study of blind patients experiencing visual hallucinations ( Hahamy, Wilf, Rosin, Behrmann, & Malach, 2021 ). The study attributes these visions to the activation of the neural networks underlying normal vision, precipitated by the hyper-excitability of the cortex to spontaneous resting-stateactivity fluctuations when it is deprived of external input. This is suggestive of the required lowering of neuronal threshold at the onset of color hallucinations predicted here. Notably, a reduction in membrane potential threshold h a sa l s ob e e na t t r i b u t e dt ot h ea c t i o no f hallucinogens ( De V os, Mason, & Kuypers, 2021 ;Varley, Carhart-Harris, Roseman, Menon, & Stamatakis, 2020 ). Finally, we note that the stability of the emergent tuning curves is determined by the bifur-cation diagram of Figure 13. This means that, in addition to expanding the region of stability in the presence of chromatic stimuli, the model 's nonlinearity allows for stable, spontaneous color hallucinations in their absence. Having thus established a Turing-like mechanism for our model 's self-organization, we end with an analogy to Turing 's original diffusion-driven formulation. In his concluding example, Turing applies the mechanism to explain the growth of an embryo along various axes of itsoriginal spherical state. This growth is driven by diffusion, directed by the “disturbing influ-ences, ”shaped by the system 's chemical and physical properties, and bounded by the sys-tem's nonlinearities. It is all too clear to see the parallels with our hue tuning model, wherein a hallucination is driven by the anisotropy of the cortical interactions, its hue determined by the initial conditions, its selectivity shaped by the cortical parameters, and its stability ensured by the thresholding nonlinearity. DISCUSSION This paper presents a neural field model of color vision processing that reconceptualizes thelink between chromatic stimuli and our perception of hue. It does so guided by the premisethat the visual cortex initiates the mixing of the cardinal L-Ma n d S-(L+M) pathways and Network Neuroscience 703Pattern 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 