10.46298/fi-2022-9736
https://fi.episciences.org/9736
Redeker, Markus
Markus
Redeker
Number Conservation via Particle Flow in One-dimensional Cellular Automata
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.
Comment: 29 pages, 6 figures
episciences.org
Nonlinear Sciences - Cellular Automata and Lattice Gases
37B15
arXiv.org - Non-exclusive license to distribute
2022-06-23
2022-10-21
2022-10-21
eng
journal article
arXiv:1907.06063
10.48550/arXiv.1907.06063
1875-8681
https://fi.episciences.org/9736/pdf
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Fundamenta Informaticae
Volume 187, Issue 1
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