Cellular Automata as Algebraic Systems
John Pedersent · Complex Systems · 1992
Infinit e cellular automat a have been st udied mostly using empirical and sta tistical techniques, wit h some combinatorial anal ysis. Here we show how concepts of universal algebra such as sub direct decomposit ion and chains of varieties can be applied to t heir st udy. Cellular auto mata wit h ultimately periodic behavior are shown to correspond to varieties of groupoids. Relat ionships between t hese varieties are analyzed.