shaped hallucinations are more salient than induced circular pat-terns, which in turn are more salient than induced spirals. Thispattern preference resembles Kenet et al. 's (2003) finding thatsome spontaneous cortical patterns recur much more often thanothers. In general, biased hallucinations and their interactions with visual stimuli obey the same rules as perception of ordi-nary stimuli; these hallucinations are spatiotemporally localizedphenomena, limited in space to the flickering field and rigidlylocked to the presence of the physical stimulus (Billock & Tsou,2007). There is evidence for temporal opponency with these same orthogonal patterns: Mac Kay (1957a, 1957b, 1965, 1978) saworthogonal hallucinations (during the off phase of flickered illu-mination) superimposed on flickered physical geometric patterns(a sequential contrast phenomenon); as discussed earlier, he sawthe same illusions as brief afterimages following prolonged view-ing of a geometric pattern and in noise streaming behind transpar-encies of these geometries. These Mac Kay effect afterimage op-ponencies are influenced by the orientation, motion, and spatialscale of the adapting features (Georgeson, 1976, 1985). A similaropponency is seen in ambiguous textures with both circular andradial correlations; for example, after adapting to a radial geome-try, a previously ambiguous pattern of random dots (Glass pat-terns) appears circular (Clifford & Weston, 2005). Two (not mu-tually exclusive) theories on functional interactions of thesegeometries have been advanced. Some researchers have noted thatgeometries like the fan shapes and concentric circles used by Mac Kay (1957a, 1957b) are the basis functions of Lie grouptheories of spatial vision (Caelli, 1977; Dodwell, 1991). Addition-ally, some masking phenomena found by Vidyasagar, Buza ´s, Kis-va´rday, and Eysel (1999) suggest that geometric opponency re-duces the persistence of some visual percepts (Wede & Francis,2006). Since a variety of drugs and clinical conditions prolongvisual persistence, it would be interesting if any of them alsoimpact geometric opponency. A possible fourth line of evidence for interactions between spontaneous pattern formation and physical stimuli stems fromsome particularly odd illusory conjunctions. Treisman (1996)treated illusory conjunctions as feature misbindings; for example,in peripheral vision, a red square and a green triangle may bemisperceived as a green square and a red triangle. One experi-ment—on perception of forbidden colors—used vertical adjacentred/green equiluminous stripes (Billock, Gleason, & Tsou, 2001;Billock & Tsou, 2010). When stabilized on the eye, the borderbetween the stripes usually collapses, and observers perceive theentire field as a novel reddish green. However, sometimes theperception of the stripes becomes multistable, and the colorsappear to change sides. Although this can be understood as anordinary illusory conjunction, Billock, Gleason, and Tsou (2001)had one subject who saw the vertical color stripes rearrange intohorizontal stripes. In this particular experiment, the tops and bot-toms of the vertical stripes were rounded (see Billock & Tsou,2004, their Figure 3), so there was no horizontal structure in theactual image for the color to misbind to. However, if humansgenerate Kenet-type cortical orientation patterns, odd occasionalmisbindings to the orientation of the Kenet patterns would beexpected. If the Kenet patterns are spatially opponent for orthog-onal geometries, misbindings would be expected in the orthogonalorientation to the original stimulus. Advanced Models of Hallucinatory Pattern Formation The spatial weighting functions ( Wijin Equation 1) used by Ermentrout and Cowan (1979) and Tass (1995, 1997) are spatially symmetric, and pattern formation arises from local reinforcementby neighboring members of the neural network; allowable patternsgenerated by the network include any doubly periodic pattern thattiles the visual cortex. Some neural network models allow aniso-tropic connectivity on cortex (Cowan, 1997; Bressloff et al., 2001,2002; Golubitsky, Shiau, & Török, 2003; Jirsa & Kelso, 2000;Qubbaj & Jirsa, 2007; Wiener, 1994), which creates new possibil-ities for modeling pattern perception. These networks could beuseful in modeling spatial opponency between radial and concen-tric patterns (Billock & Tsou, 2007). One can imagine a set of Ermentrout-Cowan-like networks, each biased to form stripes inhorizontal, vertical, or oblique angles along V1, with competitionbetween networks for the right to fire. Such a system couldproduce spatial opponency at a distance, if the vertical and hori-zontal stripe-producing networks had mutual geometrically antag-onistic long-range connections preferentially arranged along par-ticular directions on V1. Anisotropic reaction-diffusion models Figure 11. Biasing hallucinations. If a physical geometry (bold figures) is placed within a flickering field, the hallucination induced by the flicker(gray figures) is orthogonal to the physical stimulus; flickering around aphysical set of concentric circles induces hallucinatory rotating fan shapes;flickering around physical fan shapes induces wobbling or pulsating con-centric circular patterns. If the entire field flickers in phase, the hallucina-tion extends through the physical stimulus. If the flicker does not extendthrough the physical form or if the form is flickered out of phase, then thehallucination is confined to the empty region beyond the physical biasingfield. From “Neural Interactions Between Flicker-Induced Self-Organized Visual Hallucinations and Physical Stimuli,” by V. A. Billock and B. H. Tsou, 2007, PNAS: Proceedings of the National Academy of Sciences, USA, 104, p. 8492. Copyright 2007 National Academy of Sciences, USA. Reprinted with permission. 761 HALLUCINATIONS AND CORTICAL PATTERN FORMATION