Abstract
Neuronal activity in a two-dimensional net is analyzed in the neighborhood of an instability. Bifurcation theory and group theory are used to demonstrate the existence of a variety of doublyperiodic patterns, hexagons, rolls, etc., as solutions to the field equations for the net activity. It is suggested that these simple geometric patterns are the cortical concomitants of the “form constants” seen during visual hallucinosis.
Similar content being viewed by others
References
Adey, W.R., Bell, F.R., Dennis, B.J.: Effects of LSD-25, psilocybin, and psilocin on temporal lobe EEG patterns and learned behavior in the cat. Neurology 12, 591–602 (1962)
Aghajanian, G.K., Foot, W.F., Sheard, M.H.: Action of psychotogenic drugs on single midbarin raphe neurons. J. Pharmacol. Exp. Ther. 171, 178–187 (1970)
Brawley, P., Duffield, J.C.: The pharmacology of the hallucinogens. Pharm. Rev. 24, 31–66 (1972)
Cowan, J.D.: Some remarks on channel bandwidths for visual contrast detection. Neurosci. Res. Program Bull. 15, 492–517 (1977)
Cowan, J.D.: The possible role of development in the specification of the afferent geometry of the primate visual cortex (to appear) (1978)
Demetrescu, M.: Ascending inhibitory and facilitatory influences controlling primary thalamo-cortical responsiveness. Brain Res. 6, 36–47 (1967)
Dybowski, M.: Conditions for the appearance of hypnagogic visions. Kwart. Psychol. 11, 68–94 (1939)
Ermentrout, G.B., Cowan, J.D.: Temporal oscillations in neural nets. J. Math. Biol. (1978)
Fischer, B.: Overlap of receptive field centers and reptesentation of the visual field in the cat's optic tract. Vision Res. 13, 2113–2120 (1973)
Fuxe, K.: Evidence for the existence of monoamine neurons in the central nervous system. IV. The distribution of monamine terminals in the CNS. Acta Physiol. Scand. 64, Suppl. 247, 41–85 (1965)
Horowitz, M.J., Adams, J.E., Rutkin, B.B.: Evoked hallucinations in epilepsy. Psychiatr. Speculator 11, 4 (1967)
Klüver, H.: Mescal and the mechanisms of hallucination. Chicago: University of Chicago Press 1967
Krill, A.E., Alpert, H.J., Ostfield, A.M.: Effects of a hallucinogenic agent in totally blind subjects. Arch. Ophthalmol. 69, 180–185 (1963)
Lance, J.W.: Simple formed hallucinations confined to an area of specific visual defect. Brain 99, 729–734 (1976)
Penfield, W., Perot, P.: The brain's record or auditory and visual experience, a final summary and discussion. Brain 86, 595–696 (1963)
Pieri, L., Keller, H.H., Burkard, W., DaPrada, M.: Effects of lisurside and LSD on cerebral monoamine systems and hallucinosis. Nature 272, 278–280 (1978)
Richards, W.: The fortifiction illusions of migraines. Scient. Amer. 224, 88–96 (1971)
Sattinger, D.H.: Group representation theory, bifurcation theory, and pattern formation. J. Functional Analysis 28, 58–101 (1978a)
Sattinger, D.H.: Selection mechanisms for pattern formation. Arch. Rat. Mech. Analys. 66, 31–42 (1978b)
Schwartz, E.: Spatial mapping in the primate sensory projection: Analytic structure and relevance to perception. Biol. Cybernetics 25, 181–194 (1977)
Schwindt, P.C.: Membrane potential trajectories underlying motoneuron rhythmic firing at high rates. J. Neurophysiol. 36, 434–449 (1973)
Siegel, R.K.: Hallucinations. Sci. Am. 237, 132–140 (1977)
Siegel, R.K.: Cocaine hallucinations. Am. J. Psychiatry 135, 309–314 (1978)
Winters, W.D., Wallach, M.B.: During induced states of CNS excitation: a theory of hallucinosis. In: Psychotomimetric drugs, pp. 193–214. Efron, D.H. (ed.) New York: Raven Press 1970
Author information
Authors and Affiliations
Additional information
To Heinrich Klüver in memoriam
Supported in part by NIHTG 2037
Rights and permissions
About this article
Cite this article
Ermentrout, G.B., Cowan, J.D. A mathematical theory of visual hallucination patterns. Biol. Cybernetics 34, 137–150 (1979). https://doi.org/10.1007/BF00336965
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00336965