Multiway Sequential Cellular Automata

Cellular automata (CAs) are used to model rule-based evolutionary systems with standard CAs applying unitary, fixed rules to an entire generation at a time. A sequential updating asynchronous cellular automaton (CA) with more than one rule for each input sequence is studied. These multiway sequential CAs (MSCAs) can model complex systems with multiple branching rule sets where changes propagate through the system. This paper examines the case of one-dimensional, two-cell, two-branch MSCAs in order to better understand their structure and the impact of parameters. The complete set of 1296 M-type rule sets possible for this type of multiway sequential CA (MSCA) is applied to a full set of 32 initial conditions, representing all possibilities of a six-cell initial condition, generating 41472 state graphs. Machine learning is used to classify a subset of these state graphs into 10 classes. Analytical data enables characterization of these classes of graphs and investigation of the role of rule sets in these state graphs. Target distribution analysis of the M-type rule sets is performed within each class of graphs to tease out intrinsic characteristics of the classes.