170mm x 244mm Collerton c10. tex V3-11/21/2014 5:28 P. M. Page 250 250 CH10 GEOMETRIC VISUAL HALLUCINATIONS the lowest order of which generates the normal mode form cos2𝜙cos𝜃⋅cos(k⋅x) Such a form can be either contoured or noncontoured. Shortly after this work, Bressloff and I introduced a way to model V1 as a crystal-like structure, and Bressloff later applied the techniques of condensed matter physics to such a structure, whence Baker and I showed how such a structure could regularize the rather irregular patterns that the Ermentrout-Cowan mechanism actually generates. More recently, we were able to make use of a new development in the theory of large-scale neocortical activity that incorporates the effects of intrinsic fluctuations in Stochastic Wilson-Cowanequations,toshowthat V1circuitrybasedonthatused in the Ermentrout-Cowan paper, but with short-range inhibition, and long-range excitationbetweenhypercolumns, can suppresstheeffectsofintrinsicfluctuations, so that they do not by themselves trigger hallucinations. Finally, we have also describedinthischapter,workinprogressonamodelforthetriggeringofmigraine auras. 10. 5. 2 Concluding remarks Despite the progress reported above, it is clear that there are many unsolved prob-lems,andmanyunansweredquestionsconcerningvisualhallucinationsthathave,as yet,norealanswers. Thereaderisreferredto Billockand Tsou(2012)forarecent, very comprehensive review of much of the literature on the Klüver form constants. Howeveritdoesseemthatthetheorydescribedinthischapterhasonlyjustscratched the surface of the problems posed by our seeing visual hallucinations. 10. 6 References Allen, P., Larøi, F., Mc Guire, P. K. and Aleman, A. (2008) The hallucinating brain: a review of structural and functional neuroimaging studies of hallucinations. Neuro-scienceand Biobehavioral Reviews,32, 175-191. Baker, T. I. and Cowan, J. D. (2009) Spontaneous pattern formation and pinning in the primaryvisual cortex. Journalof Physiology(Paris),103, 52-68. Billock,V. A. and Tsou,B. H. (2012)Elementaryvisualhallucinationsandtheirrelation-ships toneural pattern-forming mechanisms. Psychological Bulletin,138, 744-774. Blasdel,G. G. (1992)Orientationselectivity,preference,andcontinuityinmonkeystriate cortex. Journalof Neuroscience,12, 3139-3161. Bosking,W. H.,Zhang,Y.,Schofield,B. and Fitzpatrick,D. (1997)Orientationselectiv-ityandthearrangementofhorizontalconnectionsintreeshrewstriatecortex. Journal of Neuroscience,17, 2112-2127.