Complex Systems

Point Mutations and Transitions Between Cellular Automata Attractor Basins Download PDF

Burton Voorhees
Author to whom correspondence should be addressed. Electronic mail address: burt@athabascau.ca.
Center for Science,
Athabasca University,
1 University Drive,
Athabasca, AB, Canada, T9S 3A3

Catherine Beauchemin
Department of Physics,
University of Alberta,
Edmonton, AB, Canada, T6G 2J1

Abstract

Transformations between attractor basins of binary cylindrical cellular automata resulting from mutations are considered. A tau-point mutation of a state consists in toggling tau sites in that state. Results of such mutations are described by a rule-dependent probability matrix. The structure of this matrix is studied in relation to the structure of the state transition diagram and several theorems relating these are proved for the case of additive rules. It is shown that the steady state of the Markov process defined by the probability matrix is always the uniform distribution over the state transition diagram. Some results on eigenvalues are also obtained.