also show activity in the posterior fusiform gyrus, which is known to contain concentrations of color sensitive neurons. Bexton et al. (1954) recognized from the beginning that the hallucinations re-ported for sensory deprivation were probably related to CBS(although they did not use the term); they cited similar cases in thenondemented elderly with conditions like cataract. ffytche (2008)remarked that the percepts reported by his CBS patients resembleflicker-induced hallucinations. Geometric Hallucinations and Their Potential Neural Correlates Of the three kinds of elementary hallucinations, the geometric hallucinations described by Klu ¨ver (1966) are of special interest because they are ubiquitous in conditions that lead to any kind ofelementary hallucination and because these shapes connect di-rectly to certain kinds of neural pattern-forming mechanisms. Chief among these Klu ¨ver forms are lattice and cobweb-like structures, fan shapes, concentric circles, spirals, and related three-dimensional structures like tunnels and funnels. Siegel and Jarvik(1975) proposed expanding Klu ¨ver's categories to include charac-teristic motions, but for our purposes, the actual forms are a goodstarting point; these Klu ¨ver form constants are fodder for neural theorists, and their characteristic motions and other dynamicsemerge naturally from the theoretical treatment of the forms. Ermentrout and Cowan (1979) noted that spiral, fan-shaped, andcircular Klu ¨ver hallucinations (see Figure 1) are all perceptual correlates of stripe patterns on visual cortex (see Figures 4 and 5). This stems from the nonlinear neural mapping of retina to cortex(see the Appendix): Parallel stripes of cortical activity are gener-ated by viewing physical concentric circles, fan shapes, or spirals(these cortical stripes are seen with functional imaging; see, e. g.,Figure 5). Conversely, if stripes of activity autonomously form onvisual cortex, then their orientation on cortex determines the shapeof the resulting hallucination (Ermentrout & Cowan, 1979). Scroll-ing of the cortical stripes yields rotation for fans/spirals andinward/outward movement for concentric patterns. Rotation of thestripes yields morphing between the percepts; a radial form cantwist into a spiral, which tightens until it is a set of concentriccircles. Kaleidoscopic changes between Klu ¨ver-like patterns are seen under many conditions; Sacks (1995b) estimated that mor-phological changes can occur about 10 times per second duringmigraine. More than one set of stripe patterns can be generated ata time. Superposition of simple cortical activity patterns modelsmore complicated lattice and cobweb hallucinations (Ermentrout& Cowan, 1979). Competition between coevolving cortical stripepatterns may be another route to changes in perceived form. Related stripe-like patterns arise in nature: the parallel cylindri-cal rolls of rising hot and falling cold fluid formed during fluidconvection, the intricate patterns on seashells, the spot-and-stripecamouflage adorning many animal skins (see Figures 6, 7, and 8;Bestehorn & Haken, 1991; Ermentrout, Campbell, & Oster, 1986;Kondo & Miura, 2010; Meinhardt, 2003; Murray, 1988; Turing,1952). Nothing dictates the point-by-point behavior of thesesystems—self-organized patterns arise from nonlinear dynamicinteractions of many neighboring units. To explain autonomouscortical stripe formation, Ermentrout and Cowan (1979) created anexcitatory-inhibitory neuronal network; under some conditions, ifexcitation is uniformly increased above a critical level (either byexternal stimuli or internal conditions), then this neuronal network generates parallel stripes of cortical activity. The orientation of thiscortical pattern (and its perceptual correlate) is unpredictable andcan be unstable. Basic Models of Self-Organized Hallucinatory Neural Pattern Formation Most models of cortical pattern formation build on the Ermentrout-Cowan model, a member of the class of Wilson-Cowan models used in a wide range of nonlinear dynamic neuraland perceptual problems (Ermentrout & Cowan, 1979; Wilson,1999; Wilson & Cowan, 1973). Like other spontaneous pattern-forming systems, there are two structural requirements: an asym-metry between two interacting mechanisms and a diffusion-like Figure 4. Mapping of retinal geometric patterns to cortical stripe pat-terns. Physical geometry imaged on retina (left) is mapped nonlinearly ontocortex (right), resulting in stripe patterns of neural activation on cortex. Conversely, if oriented stripes of neural activity form on cortex, theyshould evoke the corresponding hallucinatory percept on the left: the Ermentrout and Cowan (1979) thesis. Some more complicated percepts(e. g., polar webs, hexagonal lattices) can result from superposition ofdifferent cortical stripe patterns. From “Neural Interactions Between Flicker-Induced Self-Organized Visual Hallucinations and Physical Stim-uli,” by V. A. Billock and B. H. Tsou, 2007, PNAS: Proceedings of the National Academy of Sciences, USA, 104, p. 8491. Copyright 2007 Na-tional Academy of Sciences, USA. Reprinted with permission. 752 BILLOCK AND TSOU