# q-VFCA: q-state Vector-valued Fuzzy Cellular Automata

@article{Nishida2020qVFCAQV, title={q-VFCA: q-state Vector-valued Fuzzy Cellular Automata}, author={Yuki Nishida and Sennosuke Watanabe and Akiko Fukuda and Yoshihide Watanabe}, journal={J. Cell. Autom.}, year={2020}, volume={15}, pages={207-222} }

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 $q$-state CA. It is based on the vector representation of $q$-state CA, that is, the $q$-states are assigned to the standard basis vectors of the $q$-dimensional real space and the local rule can be expressed by a tuple of $q$ polynomials. Then, the $q$-state…

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