English

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

Cellular Automata and Lattice Gases 2019-10-21 v1

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.

Keywords

Cite

@article{arxiv.1910.08236,
  title  = {A hierarchical structure in the motion representation of 2-state number-conserving cellular automata},
  author = {Gil-Tak Kong and Katsunobu Imai and Toru Nakanashi},
  journal= {arXiv preprint arXiv:1910.08236},
  year   = {2019}
}

Comments

7 pages, 5 figures