Other Complications: Alternate Pattern-Formation Mechanisms and Neural Loci Complicating this picture are alternative mechanisms that could lead to hallucinatory geometric patterns. For example, considerrotating spirals and pinwheels: In the Ermentrout-Cowan model,these correspond to a pattern of oblique stripes of neural activityon cortex (angle of orientation on cortex determines spiral tight-ness), scrolling perpendicularly to the orientation of the stripes. Alternately, some systems of reactive media produce spreadingscroll-like waves that in two dimensions are actual spirals. Fohlmeister, Gerster, Ritz, and van Hemman (1995) modeled an Ermentrout-Cowan-like system that produces both stripe patterns and actual scrolling spiral waves on cortex, whose perceptualcorrelates could be hard to distinguish under some conditions. Ermentrout and Terman (2010) created a coupled neural oscillatormodel that produces rotating spiral waves on simulated cortex; anetwork of excitatory cells with time delays can behave similarly(Sacks, 1995b). Models incorporating synaptic-like time delayscan also yield temporal oscillations (ca. 10 Hz) that resemble theillusory flicker seen in CBS and visual epilepsy (Henke, Robinson,Drysdale, & Loxley, 2009). Similarly, Ermentrout (1984) and Ruleet al. (2011) noted that the Ermentrout and Cowan (1979) modelcan producing oscillations of 13-20 Hz, similar to migraine scin-tillations. Another complication is that some classes of visualhallucinations may be influenced by activity in areas other thanstriate cortex (V1). For example, some cells in cortical area V4 aresensitive to concentric circles and fan shapes (Gallant, Connor,Rakshit, Lewis, & Van Essen, 1996); V3a (and possibly V8) isactive in some migraines (Hadjikhani et al., 2001). Significantly,ffytche (2008) found increases in activity throughout visual andfrontal-parietal cortex during flicker-induced hallucinations; activ-ity in visual cortex was centered on V4. Activity in V1 was notparticularly elevated compared to nonhallucinating flicker con-trols, but the Ermentrout-Cowan model does not require a netincrease in V1 activity, but rather an increase in spatial structuringof excitatory and inhibitory activity, which is not currently image-able (as discussed above). If other cortices are involved in auton-omous spatiotemporal pattern formation, they may further compli-cate matters by feeding back their activity to V1. It would beextremely interesting to find out if perception of circular andfan-shaped hallucinations could be altered by deactivating V4temporarily (e. g., by TMS) or permanently by surgery in a patientwith pathological V4 lesions. An analogous experiment wouldmonitor migraine percepts before and after V3a and V8 deactiva-tion. It would also be desirable to monitor activity in V1 layer 6neurons. Although flicker is a fine stimulus for the LGN, ffytschefound an interesting loss of activity in LGN during flicker-inducedhallucinations, relative to flicker trials without hallucinations. Al-though LGN is often thought of as a relay station from retina tocortex, there are an order of magnitude more neurons contacting LGN from layer 6 of V1 than there are LGN cells projecting to V1. This massive feedback pathway is believed to selectively modu-late/regulate LGN sensitivity and may be activated by pattern-forming activity in V1. Because the layer 6 feedback is spatiallyspecific, it may also spatially shape the input to V1 pattern-forming mechanisms. Pattern-Formation Mechanisms in Phosphene and Fortification Percepts Much effort has gone into elucidating the self-organized pattern-formation mechanisms that underlie geometric hallucinations. Wehave already seen several connections between geometric halluci-nations, phosphenes, and fortification percepts, especially in theirspatial and temporal scales and in the ways that the same condi-tions can elicit combinations of the three percepts. Although not asmuch effort has gone into understanding the nonlinear dynamics ofphosphenes and fortifications auras, it is worthwhile to examinesome exceptions. Single spot-like phosphenes—most common forocular pressure and direct cortical electric stimulation—are oftenbest understood as focal activation of one or more neighboringneurons, within a single cortical column. They can however becreated by pattern-forming mechanisms, like Sacks's (1995b)time-delay excitatory neural network, which also models Klu ¨ver patterns. Multiple phosphenes are an interesting problem. Ermentrout-Cowan models can produce regular arrays of phos-phenes—the polyopia phenomena often noted for some clinicalconditions and often seen for drug and flicker-induced hallucina-tions. Reaction-diffusion-like mechanisms—which can model mi-graine fortification arcs (Dahlem & Chronicle, 2004)—would alsobe able to model phosphene polyopia and stripe formation invision (which resembles the spot-and-stripe formation on animalcoats that motivated reaction-diffusion theory). For example, whennonequiluminant color borders are retinally stabilized, the bor-ders can collapse, and the colors can seem to slowly diffuseacross the former boundaries, like an image made of meltingwax. As the colors flow and mix, they can form patterns, likered streaks on a green background or blue glitter on a yellowbackground (Billock, Gleason, & Tsou, 2001; Billock & Tsou,2010), much like the spotted and striped animal coats that areformed by reaction-diffusion systems (Murray, 1989; Turing,1952). Although, at first blush, diffusion seems like an oddmechanism to invoke, filling-in mechanisms are ubiquitous invision and often mimic a high-velocity diffusion-like process(see Paradiso & Nakayama, 1991, who found a fast corticalspread speed of at least 150 mm/s by using temporal masking asa probe). In this regard, the slowest color diffusion seen by Billock, Gleason, and Tsou (2001) would lie between the nor-mal very fast filling-in process and the very slow movement ofmigraine activity. Of course, given the conceptual similarity ofthe Ermentrout-Cowan model to a reaction-diffusion system, aunified model that tackles the sequential development of pho-sphenes, fortifications, and Klu ¨ver geometries within a single migraine attack should be feasible. Along these lines, it isworthwhile to consider cases that blur the distinction betweenphosphenes and Klu ¨ver patterns. The Blurry Distinction Between Phosphenes and Klu¨ver Forms As discussed earlier, phosphenes show the same kind of nonlinear scaling with position in the visual field as geometrichallucinations and migraine fortifications. When phosphenesoccur in large numbers (polyopia), they are often arranged inthe same geometries as Klu ¨ver patterns. Yet this does not exhaust the potential links between these phenomena, which764 BILLOCK AND TSOU