V.N. Biktashev 
and A.V. Holden 
November 25, 1997
Institute for Mathematical Problems in Biology,
Pushchino, Moscow Region, 142292, Russia
Department of Physiology, University of Leeds, Leeds LS2 9JT, UK
Author to whom correspondence should be addressed
We explain the phenomenon of hypermeander of spiral waves, observed in numerical experiments with various models of excitable media, as a chaotic attractor in the quotient system with respect to the Euclidean group. Such an attractor should lead to a motion of the spiral wave tip analogous to that of a Brownian particle, with mean square of displacement of the tip growing linearly at large times. This prediction is confirmed by numerical experiments with hypermeandering spiral waves.