170mm x 244mm Collerton c10. tex V3-11/21/2014 5:28 P. M. Page 244 244 CH10 GEOMETRIC VISUAL HALLUCINATIONS (a) (b) Figure 10. 23 (a) Non-contoured roll pattern. Flicker frequency 18Hz. (b) Non-contoured hexagonal pattern. Flicker frequency 8Hz. Source: Redrawnfrom Rule etal. (2011). The reader will recall that these equations can only generate non-contoured form constants. However, the results fit Purkinje's observations very well. Figure 10. 23 shows the main results (in V1 coordinates). It should be noted that low frequency stimuli (10Hz or less) generate Hexagonal planforms,whilehigherfrequencystimuligenerateperiodicstripeplanforms. There are at least two mechanisms involved in such results. The first relates to a property observedinsimulationsby Wilsonand Cowan(1973),thatof frequencydemultipli-cation, or equivalently, period doubling. This phenomenon occurs in periodically driven nonlinear equations like those introduced by Wilson and Cowan. It follows that solutions of such equations follow a low frequency flicker in a {1∶1}fash-ion,butahigherfrequencyin {2∶1}fashion,andsoon. Thesecondmechanismis more subtle. It turns out that the pattern forming mechanism that generates stripes or hexagons is controlled by the way in which the homogeneous V1 resting state losesitsstability. Thedetailsofallthisareoutsidethescopeofthisreview,butwere worked out for the Wilson-Cowan equations in Ermentrout and Cowan (1980), and elaborated in Ermentrout (1991). Ruleet al. also note that the flicker phosphenes are observed in vivid colours, so that the figures in their paper are displayed as blue stripes or blobs on yellow, orangeorgreenbackgrounds. Infactmanyoftheformconstantswehaveshownin this chapter are also seen by subjects as vividly coloured. It remains a problem to formulate and developa theory of coloured form constants. 10. 4. 5 Fortiﬁcation patterns Thefinaltopicwewillrevueistheoriginoftheimageryseenbymanypeopleduring the course of a migraine episode. The subject is well documented (Sacks, 1999).