A New Structure of 2-State Number-Conserving Cellular Automata

State-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 ...

On Universality of Radius 1/2 Number-Conserving Cellular Automata

A number-conserving cellular automaton (NCCA) is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modeling of the physical conservation laws of mass or energy. In this paper we show a construction method of radius 1/2 NCCAs. The local transition function is expressed via a singl...

Number conserving cellular automata: new results on decidability and dynamics

In the last ten years number conserving cellular automata (NCA) have received greater and greater attention. This interest is confirmed by the hundreds of papers in international conferences or journals since their introduction in [15]. They essentially model particle systems ruled by conservation laws of mass or energy with applications in a wide range of scientific disciplines. For example, t...

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.