stochastic resonance—first predicted for mathematical systems (Ditzinger, Ning, & Hu, 1994)—is not yet well documented inneural systems; there are only a few relevant models and onerelated psychophysical study. For example, in a simulation of200/H11003200 coupled neural oscillators, 1/f noise was far more efficient than white noise in inducing spatiotemporal pattern for-mation (Busch, Garcia-Ojalvo, & Kaiser, 2003; Busch & Kaiser,2003). Similarly, a noise input to Tass's (1995) model inducessimulated concentric circles that pulsate and spirals and fans thatrotate (which corresponds to scrolling of the cortical stripe pat-terns). These are the same dynamics that emerged in Golubitsky etal. 's (2003) model, but via a very different mechanism. Tass'smodel illuminates a fascinating experimental finding: Viewingdynamic fractal noise through a transparency of concentric circlesgenerates a hallucinatory rotating fan shape, while viewing iden-tical noise through a transparency of radial blades generates pul-sating circles (Billock & Tsou, 2007). The noise's statistics matter;spatially fractal noise requires much less contrast to generate thehallucinations than does spatially flat (white) noise. The temporalnoise statistics affect the hallucinatory rotation or pulsation rate. Aspects of Perceptual Pattern Formation That Require Additional Work Despite these advances, gaps remain in the study of cortical and perceptual pattern formation. Many of these gaps could be filled byimproved electrophysiological mapping/functional imaging tech-niques, but the technical problems are formidable. The moreprosaic problem involves resolution of neural events. In this re-gard, the best spatiotemporal resolution is obtained with voltage-specific dyes on exposed primate cortex (Kenet et al., 2003)—forexample, see Figure 10—but the method is unsuited for humanstudies. Conversely, imaging studies do map migraine triggerwaves in V1 and other activity in V3a (Hadjikhani et al., 2001), butnot at the resolution required to infer the percept. Biased halluci-nations (see Figure 11)—which produce stable, coarse-featuredpatterns—may be helpful here (Billock & Tsou, 2007). However,a more serious problem stems from the difficulties imposed byneural coding. Coding of Hallucinatory Features: Neural Substrates and Functional Imaging One difficulty with functional imaging is the way that the imaging signal relates to the neural activity underlying the hallu-cination. For example, in the Ermentrout-Cowan models that ex-plicitly represent the excitatory and inhibitory cell populations, thestationary patterns consist of stripes of high neural activity inwhich excitatory activity dominates, flanked by stripes of lowneural activity; such stripes—if spatiotemporally stable—shouldbe imageable. However, for scrolling patterns, which in our expe-rience are more common (e. g., rotating fans and spirals, pulsatingcircles), the inhibitory activity lags the excitatory activity, filling inthe cortical grating patterns with neural activity. Inhibitory cellsare at least as energetically demanding as excitatory cells, and so,their activity will blur the f MRI blood oxygen level-dependentsignal (and just about any kind of imaging that is not neurotrans-mitter specific), limiting detection of the coarse structure of thehallucination. Even worse for imaging are Rule et al. 's (2011)standing wave patterns, where the stripes of excitation and inhi-bition exchange positions every 50-100 ms. 7Imaging the fine structure is more difficult still; Bressloff et al. 's (2001, 2002) work suggests that while Ermentrout-Cowan cortical stripe formationdetermines the overall geometry of hallucinations, the specificneurons activated in those stripes determine what that geometrylooks like: its texture, depth, contrast, color, and more. It isinteresting then that many experimental conditions induce pastel orgrey hallucinatory features, suggesting small asymmetries in theactivation of complementary neural populations. In the early visualsystem, perceptually opponent mechanisms often balance one an-other; for example, activated off-response cells signal featuresdarker than their background, while activation of on-responseneurons should trigger perception of a bright feature. This codingof images by complementary neural populations imposes limita-tions on imaging those responses. Consider, for example, a light-and-dark hallucination generated by patterns of on-and off-cortical cell activity, respectively; if both yield the same imageableactivity on V1, then the structure of the percept would not beresolved using current functional imaging approaches. 8 However, there are exceptions to the population balance rule. Brilliant colors are often reported in drug-induced hallucinations. Similarly, migraine fortifications are reported as bright, oftenblindingly so. Of course, this may be a reporting bias—one speaks of the bright fortification lines and not of the dark spaces betweenthem. Indeed, some drawings of migraine fortifications depict theindividual fortifications as more like grating patches than linesegments (e. g., Dahlem & Chronicle, 2004, p. 358, their Figure 5),suggesting that both on-and off-neurons can be activated duringmigraine, but out of phase with one another (a spatiotemporalphase shift could also account for the perceptual scintillations seenin migraine fortifications). This is essentially the same spatiotem-poral phase shift considered above for scrolling of the Ermentrout-Cowan patterns, and it imposes the same filling-in of imageableactivity problem. Similar problems will limit ability to discernhallucinatory texture, color, motion, and depth until advances inimaging overcome these limitations. The nuances of hallucinatory perception just discussed also highlight a related problem. Although we now understand whypercepts like spirals, fan shapes, and concentric circles form andcan readily imagine why such forms would take on attributes likecolor and depth, we have relatively little understanding aboutdifferences between subjects or conditions in inducing color anddepth. For example, in flicker-induced hallucinations, some ob-servers describe the illusory colors as vivid and even unearthly,while other observers (including, alas, ourselves) see the colors aspastels. Small differences in experimental design also seem to havelarge effects: Most biased hallucinations are achromatic Klu ¨ver forms, although subjective colors may appear in the inducing fields(Billock & Tsou, 2007). 7A standing wave (whose psychophysical correlate is a contrast-reversing grating) is mathematically equivalent to two traveling waves, propagating through one another in opposite directions (Kelly, 1985). 8Tootell et al. 's (1998) retinocortical mapping cleverly avoided this problem by using an image (see Figure 3) whose voids were designed to elicit minimal neural response, while the image features (made of contrast-reversing checks) were designed to create maximal imaging signals. 763 HALLUCINATIONS AND CORTICAL PATTERN FORMATION