Coalescing Cellular Automata -- Synchronizing CA by Common Random Source and Varying Asynchronicity
Cellular Automata and Lattice Gases
2007-12-13 v1
Abstract
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both configurations become identical after a reasonable time. We prove coalescence for two elementary rules, non coalescence for two other, and show that there exists infinitely many coalescing CA. We then conduct an experimental study on all elementary CA and show that some rules exhibit a phase transition, which belongs to the universality class of directed percolation.
Cite
@article{arxiv.0712.1992,
title = {Coalescing Cellular Automata -- Synchronizing CA by Common Random Source and Varying Asynchronicity},
author = {Jean-Baptiste Rouquier and Michel Morvan},
journal= {arXiv preprint arXiv:0712.1992},
year = {2007}
}