eng
episciences.org
Fundamenta Informaticae
0169-2968
1875-8681
2022-10-21
Volume 187, Issue 1
10.46298/fi-2022-9736
9736
journal article
Number Conservation via Particle Flow in One-dimensional Cellular Automata
Markus Redeker
A number-conserving cellular automaton is a simplified model for a system of
interacting particles. This paper contains two related constructions by which
one can find all one-dimensional number-conserving 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 non-deterministic
number-conserving rules, are treated briefly at the end.
https://fi.episciences.org/9736/pdf
Nonlinear Sciences - Cellular Automata and Lattice Gases
37B15