Number Conservation via Particle Flow in Onedimensional Cellular Automata
Abstract
A numberconserving cellular automaton is a simplified model for a system of interacting particles. This paper contains two related constructions by which one can find all onedimensional numberconserving cellular automata with one kind of particle. The output of both methods is a "flow function", which describes the movement of the particles. In the first method, one puts increasingly stronger restrictions on the particle flow until a single flow function is specified. There are no dead ends, every choice of restriction steps ends with a flow. The second method uses the fact that the flow functions can be ordered and then form a lattice. This method consists of a recipe for the slowest flow that enforces a given minimal particle speed in one given neighbourhood. All other flow functions are then maxima of sets of these flows. Other questions, like that about the nature of nondeterministic numberconserving rules, are treated briefly at the end.
 Publication:

arXiv eprints
 Pub Date:
 July 2019
 DOI:
 10.48550/arXiv.1907.06063
 arXiv:
 arXiv:1907.06063
 Bibcode:
 2019arXiv190706063R
 Keywords:

 Nonlinear Sciences  Cellular Automata and Lattice Gases;
 37B15
 EPrint:
 29 pages, 6 figures