Using the concept of Boolean derivative of a cellular automaton we study the local damage spreading and present a definition of the maximal Lyapunov exponent. We calculate this exponent for all minimal elementary one dimensional cellular automata and for totalistic cellular automata of range two and three. A random matrix approximation describes the behavior of “chaotic” cellular automata and predicts a directed percolationtype phase transition.
Maximal Lyapunov Exponent for 1D Boolean Cellular Automata / Bagnoli, F.; Rechtman, R.; Ruffo, S.. - 396:(1993), pp. 19-28. (Intervento presentato al convegno NATO Advanced Study Institute on `Cellular Automata and Cooperative Systems' tenutosi a Les Houches, France nel June 22 to July 2, 1992) [10.1007/978-94-011-1691-6_3].
Maximal Lyapunov Exponent for 1D Boolean Cellular Automata
Ruffo, S.
1993-01-01
Abstract
Using the concept of Boolean derivative of a cellular automaton we study the local damage spreading and present a definition of the maximal Lyapunov exponent. We calculate this exponent for all minimal elementary one dimensional cellular automata and for totalistic cellular automata of range two and three. A random matrix approximation describes the behavior of “chaotic” cellular automata and predicts a directed percolationtype phase transition.| File | Dimensione | Formato | |
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