Time-evolution of the Rule 150 cellular automaton activity from a Fibonacci iteration

Details Time-evolution of the Rule 150 cellular automaton activity from a Fibonacci iteration Time-evolution of the Rule 150 cellular automaton activity from a Fibonacci iteration

2004-10-19

arxiv.org/abs/math/0410429v1

Journal of Mathematical Physics 49, 062701 (2008)

Mathematics

Combinatorics

4 pages (3 figs included)

Scientific paper

10.1063/1.2939398

The total activity of the single-seeded cellular rule 150 automaton does not follow a one-step iteration like other elementary cellular automata, but can be solved as a two-step vectorial, or string, iteration, which can be viewed as a generalization of Fibonacci iteration generating the time series from a sequence of vectors of increasing length. This allows to compute the total activity time series more efficiently than by simulating the whole spatio-temporal process, or even by using the closed expression.

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