dermaier (1976) found that it was easier to electrically stimulate geometric hallucinations at high altitudes, presumably as a sideeffect of hypoxia. This is interesting because hypoxia alsofacilitates triggering the cortical spreading depression phenom-enon linked to migraine (Dahlem & Mu ¨ller, 2004; Grafstein, 1963; Lea ˜o, 1963). Some transcranial electric stimuli may also inadvertently excite the eye (Motokawa, 1970; Paulus, 2010);the persistence of hallucinations after temporarily pressure-blinding the eyes is a useful check. Direct electric stimulation of the human cortex (V1-V3) was used by Penfield and Rasmussen (1950) while locating surgi-cally excisable epileptic foci. Stimulation of V1 usually leads tosmall colored phosphenes. Stimulation outside V1 often leadsto moving colorless phosphenes. Pulse trains are more effectivethan single stimuli or direct current, and phosphene thresholdsare smallest in cortical layers 4-6 (Bak et al., 1990). Pulsetrains longer than about 15 s become ineffective (Dobelle,Mladejovsky, Evans, Roberts, & Girvin, 1976; Dobelle, Quest,Autunes, Roberts, & Girvin, 1979). Electrode separations of 1mm or less result in a single phosphene (Bak et al., 1990),consistent with estimates of human cortical column size. Sur-face electrodes tend to induce flicker, while deeper electrodestend to induce steady deeply colored circular phosphenes. In-creasing stimulus strength raises the phosphene's brightnesswhile reducing its size (Bak et al., 1990, and Evans, Gordon,Abramov, Mladejovsky, & Dobelle, 1979, found a logarithmicrelation for phosphene brightness). Brindley and Lewin (1968)used arrays of phosphene-inducing electrodes while developinga neural prosthetic for the blind. Maps of phosphene size as afunction of electrode position can be used to estimate corticalmagnification: Phosphenes generated in central vision are punc-tuate, while phosphenes in peripheral vision may be severaldegrees wide (Dobelle et al., 1976, 1979). TMS is a special case, intermediate to transcranial electric stimulation and direct cortical stimulation using small elec-trodes. An alternating magnetic field—applied across theskull—induces electric currents in the cortex. Unlike transcra-nial electric stimulation, TMS stimuli are generally painless. Special antennas localize stimulation to several centimeters ofcortical area, which, although not as precise as those induced bydirect cortical electric stimulation, is more convenient; based onother induced hallucinations, the increased spatial extent ofstimulation is likely to bias the system to geometric hallucina-tions rather than simple phosphenes. In Marg and Rudiak(1994) and Kammer, Puls, Erb, and Grodd (2005), the mostcommon percepts were wedges and butterfly patterns (doublewedges); grids and hexagonal lattice patterns were also re-ported. Single pulses of TMS do not produce illusory features ininexperienced observers (Kammer et al., 2005), but short trainsof stimulation (two to five pulses) reliably produce hallucina-tions in all observers (Boroojerdi et al., 2002; Ray, Meador,Epstein, Loring, & Day, 1998). The position and shape of thephosphene in Krammer et al. 's experiment did not vary muchwith the skull position of the coil over occipital cortex; toexplain this invariance, Kammer et al. speculated that their TMS activated cortex indirectly, via the optic radiations to V1and back-projecting fibers from V2 and V3 onto V1. Flicker-Induced Hallucinations Flicker-induced hallucinations were discovered by Purkinje (1819/1823) and Brewster (1834). Purkinje evoked colored pat-terns while waving his spread fingers between a bright light andhis shut eyes. Brewster (the inventor of the kaleidoscope) sawillusory colored patterns while rushing past a sunlit fence with hiseyes shut—a result enjoyably replicable for passengers on fastdrives through sunlit forests (Billock & Tsou, 2010). Both casesillustrate the optimal stimulus for flicker-induced hallucina-tions—a strong source of spatially homogeneous temporal modu-lation (closed eyes are relatively uniform diffusers). Later studiesby Fechner (1838) and others used rotating black-and-white sectordisks: At a sufficiently high rotation rate, the individual rotatingsectors fuse into a uniform flickering gray. Many observers seehexagonal pastel-colored patterns on the disk under these circum-stances, but other patterns are reported as well. Most modernstudies of flicker-induced hallucinations use stroboscopic illumi-nation of a uniform surface (a ganzfeld) or the flickering emptyscreen of a CRT. In clinical studies, illusory forms and colors area frequently reported side effect of flicker ERG/electroencephalo-gram (EEG) tests. W. G. Walter (1956) stimulated thousands ofpatients with stroboscopic-illuminated ganzfelds, all of whom re-ported illusory colors, movements, and patterns; the optimumfrequency for evoking the effects varied greatly between observ-ers, and the most common patterns were moving concentric ringsand spoke patterns. Mundy-Castle (1953) made the same claimsfor his 1,000 subjects. Many studies find that flicker rates of about4-25 Hz elicit illusory color and forms (Brown & Gebhard, 1948;Freedman & Marks, 1965; Mundy-Castle, 1953; Remole, 1971,1973; Smythies, 1959a, 1959b, 1960; V. J. Walter & Walter,1949). In our experience, hallucinations do occur at low flicker rates but are more salient at moderate rates (ca. 10-20 Hz). The form ofthe hallucinated pattern may be frequency dependent (e. g.,Allefeld, Pu ¨tz, Kastner, & Wackermann, 2011; Becker & Elliot, 2006; Young, Cole, Gamble, & Rayner, 1975). There seems to belittle consistency between studies, possibly due to differences instimulation techniques. The most ambitious attempt to determinefrequency dependency is Allefeld et al. 's (2011) strobed-ganzfeldstudy. They plotted frequency-of-seeing distributions for about3,000 occurrences of 17 different spatial percepts and found thatthey occur mostly in the 5-26 Hz range. Several of their 17perceptual patterns correspond to Klu ¨ver's forms (and Ermentrout-Cowan cortical stripe formation). Both spirals and concentriccircles (ripples) have perceived frequency distributions that peak atabout 15-18 Hz. Three separate categories correspond to radialhallucinations (wheel, sun, star) and have peaks between about 7and 18 Hz. Hexagonal (honeycomb) and rectilinear (raster) latticeshave peaks near 15 and 30 Hz, respectively. Phosphene-like illu-sions (spot, organic) are more common at 25-30 Hz. Color in thesehallucinations is most common at 11-18 Hz (much higher than for Fechner-Benham illusory colors, which are most vivid for flickerrates near 6 Hz). Remole (1971, 1973) measured luminance contrast thresh-olds for flicker-induced illusory geometric patterns as a func-tion of temporal frequency; some of these tuning functionsresemble resonance curves. For binocular vision, his subjectshad lower thresholds for flash rates of 10-18 Hz. For monoc-749 HALLUCINATIONS AND CORTICAL PATTERN FORMATION