Densities and entropies in cellular automata
Pierre Guillon, Charalampos Zinoviadis
TL;DR
This paper characterizes which real numbers can be topological entropies of 1D and 2D cellular automata using computability theory, building on prior work on multidimensional SFT.
Contribution
It provides new computability-theoretic characterizations of topological entropies for cellular automata in one and two dimensions.
Findings
Identifies which real numbers are attainable as entropies
Extends prior work on multidimensional SFT to cellular automata
Establishes computability conditions for entropy values
Abstract
Following work by Hochman and Meyerovitch on multidimensional SFT, we give computability-theoretic characterizations of the real numbers that can appear as the topological entropies of one-dimensional and two-dimensional cellular automata.
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Taxonomy
TopicsCellular Automata and Applications · Computability, Logic, AI Algorithms · Mathematical Dynamics and Fractals