EVENTUALLY NUMBER-CONSERVING CELLULAR AUTOMATA

Eventually Number-Conserving Cellular Automata

We present a preliminary study of a new class of two-input cellular automaton rules called eventually number-conserving rules characterized by the property of evolving after a finite number of time steps to states whose number of active sites remains constant. Viewed as models of systems of interacting particles, these rules obey a kind of Darwinian principle by either annihilating unnecessary ...

Number-conserving cellular automata I: decidability

We prove that de6nitions of number-conserving cellular automata found in literature are equivalent. A necessary and su9cient condition for cellular automata to be number-conserving is proved. Using this condition, we give a quasi-linear time algorithm to decide number-conservation. c © 2002 Elsevier Science B.V. All rights reserved.

State-Conserving Cellular Automata

Solutions for certain number-conserving deterministic cellular automata.

We explain the unexpected behavior of the generalizations of cellular automation traffic models introduced in [H. Fukś and N. Boccara, Int. J. Mod. Phys. C 9, 1 (1998)]. We analyze the steady-state flow in R(m,k) as a function of the initial density; we show that these rules correspond to a system with an infinite number of different kinds of virtual particles interacting according to complex a...

Fluctuation-driven computing on number-conserving cellular automata

A number-conserving cellular automaton (NCCA) is a cellular automaton where the states of cells are denoted by integers, and the sum of all numbers in a configuration is conserved throughout its evolution. It has been widely used to model physical systems ruled by conservation law of mass or energy. Imai et al. (2002) showed that an NCCA’s local transition function can be effectively translated...