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Remarks on the Critical Behavior of Second Order Additive Invariants in Elementary Cellular Automata

Fukś H.

Fundamenta Informaticae

2007

Vol. 78, nr 3

329-341

We present results of some numerical investigations of second order additive invariants in elementary cellular automata rules. Fundamental diagrams of rules which possess additive invariants are either linear or exhibit singularities similar to singularities of rules with first-order invariant. Only rules which have exactly one invariants exhibit singularities. At the singularity, the current decays to its equilibrium value as a power law ta, and the value of the exponent a obtained from numerical simulations is very close to -1/2. This is in agreements with values previously reported for number-conserving rules, and leads to a conjecture that regardless of the order of the invariant, exponent a has a universal value of 1/2.

Modele perkolacji

Fukś H.

Wiadomości Naftowe i Gazownicze

2006

R. 9, Nr 7 (99)

14-16

Number-conserving cellular automaton rules

Boccara N., Fukś H.

Fundamenta Informaticae

2002

Vol. 52, nr 1-3

1-13

A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two different forms of simpler and more visual representations of these rules are given, and their flow diagrams are determined. Various examples are presented and applications to car traffic are indicated. Two nontrivial three-state three-input self-conjugate rules have been found. They can be used to model the dynamics of random walkers.