$q$-VFCA: $q$-state Vector-valued Fuzzy Cellular Automata
Abstract
Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for -state CA. It is based on the vector representation of -state CA, that is, the -states are assigned to the standard basis vectors of the -dimensional real space and the local rule can be expressed by a tuple of polynomials. Then, the -state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the -dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.
Keywords
Cite
@article{arxiv.2002.02653,
title = {$q$-VFCA: $q$-state Vector-valued Fuzzy Cellular Automata},
author = {Yuki Nishida and Sennosuke Watanabe and Akiko Fukuda and Yoshihide Watanabe},
journal= {arXiv preprint arXiv:2002.02653},
year = {2020}
}
Comments
16 pages