Related papers: Number-conserving cellular automaton rules
We show that there exists a one-to-one correspondence between the set of number-conserving cellular automata (CA) with $q$ inputs and the set of balanced sequences with $q$ terms. This allows to enumerate number-conserving CA. We also show…
This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the…
A number-conserving cellular automaton 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 modelization of the physical…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for \cas to be number-conserving is proved. Using this condition, we give a linear-time algorithm to…
We present a preliminary study of a new class of two-input cellular automata called eventually number-conserving cellular automata characterized by the property of evolving after a finite number of time steps to states whose number of…
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…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
We present necessary and sufficient conditions for a cellular automaton with a von Neumann neighborhood of range one to be number-conserving. The conditions are formulated for any dimension and for any set of states containing zero. The use…
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
This paper studies the number conservation property of 1-dimensional non-uniform cellular automata (CAs). In a non-uniform cellular automaton (CA), different cells may follow different rules. The present work considers that the cells follow…
In this paper a cellular automata model for one-lane traffic flow is presented. A new set of rules is proposed to better capture driver reactions to traffic that are intended to preserve safety on the highway. As a result, drivers behavior…
This paper concerns $d$-dimensional cellular automata with the von Neumann neighborhood that conserve the sum of the states of all their cells. These automata, called number-conserving or density-conserving cellular automata, are of…
We investigate number conserving cellular automata with up to five inputs and two states with the goal of comparing their dynamics with diffusion. For this purpose, we introduce the concept of decompression ratio describing expansion of…
If X is a discrete abelian group and B a finite set, then a cellular automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts. If g is a real-valued function on B, then, for any b in B^X, we define G(b) to be the sum…
Invertible cellular automata are useful as models of physical systems with microscopically revesible dyanmics. There are several well-understood ways to construct them: partitioning rules, second-order rules, and alternating-grid rules. We…
A family of multi-value cellular automaton (CA) associated with traffic flow is presented in this paper. The family is obtained by extending the rule-184 CA, which is an ultradiscrete analogue to the Burgers equation. CA models in the…
We investigate dynamics of the cellular automaton rule 142. This rule possesses additive invariant of the second order, namely it conserves the number of blocks 10. Rule 142 can be alternatively described as an operation on a binary string…
We investigate critical properties of a class of number-conserving cellular automata (CA) which can be interpreted as deterministic models of traffic flow with anticipatory driving. These rules are among the only known CA rules for which…