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arXiv · 1910.08236

A hierarchical structure in the motion representation of 2-state number-conserving cellular automata

Gil-Tak Kong·Katsunobu Imai·Toru Nakanashi
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Abstract

A one-dimensional two-state number-conserving cellular automaton (NCCA) is a cellular automaton whose states are 0 or 1 and where cells take states 0 and 1 and updated their states by the rule which keeps overall sum of states constant. It can be regarded as a kind of particle based modeling of physical systems and has another intuitive representation, motion representation, based on the movement of each particle. We introduced a kind of hierarchical interpretation of motion representations to understand the necessary pattern size to each motion. We show any NCCA of its neighborhood size n can be hierarchically represented by NCCAs of their neighborhood size from n-1 to 1.

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Gil-Tak Kong, Katsunobu Imai, Toru Nakanashi. 2019-10-18. A hierarchical structure in the motion representation of 2-state number-conserving cellular automata. https://arxiv.org/abs/1910.08236

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