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

On the Measure Entropy of Additive Cellular Automata f

Arts and Sciences Faculty, Department of Mathematics, Harran University; 63100, Şanlıurfa, Turkey
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

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MDPI and ACS Style

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

AMA Style

Akın H. On the Measure Entropy of Additive Cellular Automata f. Entropy. 2003; 5(2):233-238.

Chicago/Turabian Style

Akın, Hasan. 2003. "On the Measure Entropy of Additive Cellular Automata f." Entropy 5, no. 2: 233-238.

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