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ECA rule 26, a member of Wolfram's class IV and Chua's hyper Bernoulli shift rules, defines infinitely many subsystems and possesses rich and complex dynamics including an infinite number of gliders and a catalog of glider collisions. Precisely, it holds positive topological entropies and topologically transitivity on the infinitely many subsystems, and is topologically mixing on another three subsystems,...
In this paper, we deal with the global equivalence classification of one-dimensional cellular automata (CA) with nearest-nearest neighborhoods. We present a theoretical classification of all rules through the two homeomorphisms identified in. we demonstrate the 30 global equivalence classes of 64 additive rules, and show that in the same equivalence class they have the same number of independent connected...
This paper provides a symbolic dynamics perspective to Chua's topologically-distinct complex Bernoulli-shift rules 18, 122, 126 and 146. Through this work, a rigorous analysis of their global attractors is conducted in the space of bi-infinite symbolic sequences. Based on the concepts of blocking transformation and releasing transformation, their chaotic dynamics is further uncovered, including topological...
In this paper, the dynamics of elementary cellular automata rule 61 is investigated in the bi-infinite symbolic sequence space. This work provides the glider properties and the interactions in rule 61, including several natural gliders, a catalog of gliders and glider collisions, which were found in Wolfram's complex rules 110 and 54 before. In addition, It is also proved that rule 61 defines three...
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