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Entropy 2003, 5(2), 233-238; doi:10.3390/e5020233
Article

On the Measure Entropy of Additive Cellular Automata f

Received: 5 February 2003 / Accepted: 12 June 2003 / Published: 30 June 2003
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Abstract

We show that for an additive one-dimensional cellular automata f on space of all doubly infinitive sequences with values in a finite set S = {0, 1, 2, ..., r-1}, determined by an additive automaton rule [equation] (mod r), and a f-invariant uniform Bernoulli measure μ, the measure-theoretic entropy of the additive one-dimensional cellular automata f with respect to μ is equal to hμ (f) = 2klog r, where k ≥ 1, r-1∈S. We also show that the uniform Bernoulli measure is a measure of maximal entropy for additive one-dimensional cellular automata f.
Keywords: Cellular Automata; Measure Entropy; Topological Entropy Cellular Automata; Measure Entropy; Topological Entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Akın, H. On the Measure Entropy of Additive Cellular Automata f. Entropy 2003, 5, 233-238.

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