2026/06/15 by Akiko Fukuda, Sennosuke Watanabe, Yuki Nishida +1
Computer Science · Engineering · #Cellular Automata and Applications #Control and Stability of Dynamical Systems #Traffic control and management
paper · pdf · doi:10.25088/complexsystems.35.2.119
In this paper, the number-conserving rules for second-order three-neighbor binary cellular automata (SOCAs) are discussed. The SOCAs include the well-known elementary cellular automata and elementary reversible cellular automata and have a total of 2 64 local rules. We show that the number of number-conserving SOCAs is limited to 74 through a polynomial representation of the local rules. A concrete description of the polynomial representation for 15 representative rules is provided. In addition, we establish a necessary and sufficient condition for each SOCA to be number conserving. This condition can be regarded as a discrete version of the flux form in fluid dynamics.