“windows on the visual brain. ” Second, elementary hallucinations illustrate an important general principle in cognitive science. It isnow well recognized that complex systems, such as the humanbrain, have collective properties that are not inherent in the indi-vidual neural elements; it has become common to ascribe somecognitive behaviors as emergent properties of the collective sys-tem. However, such attributions are seldom well worked out andare most often reasoned by analogy to better studied complexphysical systems. Elementary hallucinations—and especially geo-metric hallucinations—provide particularly well-worked-out ex-amples of a neural emergent behavior (self-organized spatiotem-poral pattern formation) that corresponds to specific percepts. Third, a rather perverse aspect of the study of the human brain asa complex system is that the brain typically behaves in a decep-tively stable and veridical fashion—much like a linear system; ifwe want to understand the brain as a nonlinear dynamic complexsystem we need to push it outside of its normal pseudolinearregime. 1Perceptual catastrophe then becomes a tool of systems identification. Finally, recent advances in neuroscience have given new importance to understanding the relationship betweenstimulus-driven and autonomous neural pattern formation. A con-vergence of research in complexity theory, neural modeling, visualpsychophysics, and functional brain imaging dramatically ad-vances understanding of perceptual pattern formation and high-lights interactions between intrinsic neural activity and physicalstimulation. Hallucinatory Conditions and the Percepts They Induce An Overview of Elementary Hallucinatory Visual Percepts This review focuses on elementary hallucinations and excludes complex imagery associated with dreams, dementia, delirium, andthe latter phases of drug intoxication and sensory deprivation(useful reviews of complex hallucinations include Aleman &Larøi, 2008; Collerton, Perry, & Mc Keith, 2005; Horowitz,1978). 2We also exclude the fascinating disturbances of shape, size, motion, and color that accompany fever and neurological disorders (e. g., the Alice in Wonderland syndrome that can heraldmononucleosis). An amazing variety of external and internal con-ditions lead to elementary hallucinations (see Figure 1 and Table1). A partial list includes migraine, epilepsy, hypoglycemia, theearly stages of some drug intoxications, ocular pressure, retinaland cortical electric stimulation, transcranial magnetic stimulation(TMS), and photopic stimulation, especially by uniform flickeringlights. The ubiquity, ease of generation, and geometric nature ofthese hallucinations have been a clue to neural modeling and agoad to perceptual experimentation. There are three basic types ofelementary hallucination: phosphenes, geometric forms, and forti-fications. The simplest illusory forms are phosphenes—usuallysmall spots of light—often induced by focal stimulation of the eyeor brain (e. g., by ocular pressure, electricity, and, more exotically,cosmic rays; Sannita, Narici, & Picozza, 2006). Phosphenes varyin size with position in the visual field and have a variety ofshapes, colors, and movements. The ability to generate phospheneshas been an opportunity to those who would create visual pros-theses for the blind and a nuisance for those who would keep the induced percepts simple. Often, phosphenes are induced in greatnumbers (polyopia) and are organized by some geometric principle(see, e. g., Figure 1E); they may appear to be hexagonally packedor to be texture elements on some greater geometric figure. Themost common geometric figures—the Klu ¨ver forms—are lattices (often hexagonal), polar webs, fan shapes, pinwheels, spirals,concentric circles, and some three-dimensional analogues (tunnels,funnels, etc. ). Fortifications are bright flashing serrated arc-shapedpatterns often seen in migraine; occasionally, similar zigzag forms,like a piece of a fortification arc, are seen in epileptic seizure,hypoglycemia, and other conditions (Klu ¨ver, 1966; Purkinje, 1819/1823). When hallucinations accompany migraine or epi-lepsy, they are referred to clinically as auras. Migraine and Fortification Illusions Migraine hallucinations range from Klu ¨ver's geometric forms to complex multisensory hallucinations (which resemble temporal-lobe epilepsy). Even within an observer, more than one hallucina-tion can occur; for example, Oliver Sacks and John Herschelreported both Klu ¨ver geometries and fortification patterns, some-times during the same attack (Sacks, 1995a). In subjects experi-encing more than one percept, phosphenes are generally seenbefore fortifications, which are seen before Klu ¨ver patterns (Sacks, 1995b); geometric patterns, like lattices, are also sometimesglimpsed between fortification features. However, as fortificationauras are considered characteristic of migraine, we focus on for-tifications here. Fortifications are bright line segments set atroughly 60° angles to one another along a vertical arc (see Figure1H). In migraine, many patients report that the line segmentsflicker at about 10 Hz, but most patients have no experience inaccurately naming flicker rates. Crotogino, Feindel, and Wilkinson(2001) flicker-matched migraine scintillations to a physical stan-dard in 11 observers: The average matched scintillation rate was17. 8 Hz, and individual subjects made consistent flicker matchesacross attacks. The segments are usually bright white, but colorscan sometimes be seen between them (Sacks, 1995a) or on theirtips, like match-ends; red, yellow, and blue, in that order, are mostcommon (Richards, 1971). The jagged structure resembles an oldstyle of fortification with many angled sides to deprive primitivewall-breaching artillery of a clean nonglancing shot. The illusiongenerally starts near the fovea in one visual hemifield and movesslowly toward the periphery. Near the fovea, the angled featuresare small, and the arc is nearly circular. The angles between theserrations are between 45° and 60°. As the arc moves toward theperiphery, its individual angular features enlarge, and the arcstraightens into a nearly vertical shape that appears to move morequickly through the visual field. Dahlem and Mu ¨ller's (2003) 1The required push may not be very large. There is some evidence that the cortex is critically poised, in the sense that relatively small changes can trigger avalanches of neuronal activity (Plenz & Thiagarajan, 2007; Wer-ner, 2007). This is in accord with the relatively modest amount of stimu-lation needed to induce some hallucinations. 2Some investigators report that complex hallucinations can develop from simpler ones (e. g., a geometric pattern of radiating lines becomes the legs of a spider upon introspection; Horowitz, 1978; Hughlings Jackson,1958). 745 HALLUCINATIONS AND CORTICAL PATTERN FORMATION