A New Structure of 2-State Number-Conserving Cellular Automata

Abstract

Two-state number-conserving cellular automaton (NCCA) is a cellular automaton of which cell states are 0 or 1, and the total sum of all the states of cells is kept for any time step. It is a kind of particle-based modeling of physical systems. We introduce a new structure of its value-1 patterns, which we call a “bundle pair” and a “bundle quad”. By employing this structure, we show a relation between the neighborhood size n and n - 2 NCCAs.