Biological Cybernetics

, Volume 34, Issue 3, pp 137–150

A mathematical theory of visual hallucination patterns

  • G. B. Ermentrout
  • J. D. Cowan

DOI: 10.1007/BF00336965

Cite this article as:
Ermentrout, G.B. & Cowan, J.D. Biol. Cybernetics (1979) 34: 137. doi:10.1007/BF00336965


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.

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • G. B. Ermentrout
    • 1
  • J. D. Cowan
    • 1
  1. 1.Department of Biophysics and Theoretical BiologyThe University of ChicagoChicagoUSA
  2. 2.Mathematical Research Branch, NIAMDDNIHBethesdaUSA

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