93 citations · 803 across the 39 of their papers we have counts for
26 papers · 1 filter
Approximating dynamics of a number-conserving cellular automaton by a finite-dimensional dynamical system
Henryk Fukś, Yucen Jin
The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely-dimensional system. While it is well known that this approx…
Four state deterministic cellular automaton rule emulating random diffusion
Henryk Fukś
We show how to construct a deterministic nearest-neighbour cellular automaton (CA) with four states which emulates diffusion on a one-dimensional lattice. The pseudo-random numbers…
Explicit solution of the Cauchy problem for cellular automaton rule 172
Henryk Fukś
Cellular automata (CA) are fully discrete alternatives to partial differential equations (PDE). For PDEs, one often considers the Cauchy problem, or initial value problem: find the…
Orbits of Bernoulli Measures in Cellular Automata
Henryk Fukś
We discuss how to construct shift-invariant probability measures over the space of bisequences of symbols, and how to describe such measures in terms of block probabilities. We the…
Explorations of ternary cellular automata and ternary density classification problems
H. Fukś, R. Procyk
While binary nearest-neighbour cellar automata (CA) have been studied in detail and from many different angles, the same cannot be said about ternary (three-state) CA rules. We pre…
Evaluating the Quality of Local Structure Approximation Using Elementary Rule 14
Henryk Fukś, Francis Kwaku Combert
Cellular automata (CA) can be viewed as maps in the space of probability measures. Such maps are normally infinitely-dimensional, and in order to facilitate investigations of their…