Point Mutations and Transitions Between Cellular Automata Attractor Basins

Details Point Mutations and Transitions Between Cellular Automata Attractor Basins Point Mutations and Transitions Between Cellular Automata Attractor Basins

2003-06-17

arxiv.org/abs/nlin/0306033v1

Complex Systems, 15(1), 2004

Nonlinear Sciences

Cellular Automata and Lattice Gases

42 pages, 3 figures. Requires AMSmath and elsart.cls. Submitted for publication in the special issue of Theoretical Computer S

Scientific paper

We consider transformations between attractor basins of binary cylindrical cellular automata resulting from mutations. A t-point mutation of a state consists in toggling t 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.

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