Related papers: Conservation Laws in Cellular Automata
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
Reversible Cellular Automata (RCA) are a particular kind of shift-invariant transformations characterized by a dynamics composed only of disjoint cycles. They have many applications in the simulation of physical systems, cryptography and…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…
Neural cellular automata (Neural CA) are a recent framework used to model biological phenomena emerging from multicellular organisms. In these systems, artificial neural networks are used as update rules for cellular automata. Neural CA are…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a…
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
In previous works, hexagonal cellular automata (CA) have been studied as a variation of the famous Game of Life CA, mainly for spiral phenomena simulations; where the most interesting constructions are related to the Belousov-Zhabotinsky…
Cellular automaton (CA) approach is an important theoretical framework for studying complex system behavior and has been widely applied in various research field. CA traffic flow models have the advantage of flexible evolution rules and…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
Three reasonable hypotheses lead to the thesis that physical phenomena can be described and simulated with cellular automata. In this work, we attempt to describe the motion of a particle upon which a constant force is applied, with a…
This article presents a new characterization of controllability and regional controllability of Deterministic Cellular Automata (CA for short). It focuses on analyzing these problems within the framework of control theory, which have been…
A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…
The cellular automata with local permutation invariance are considered. We show that in the two-state case the set of such automata coincides with the generalized Game of Life family. We count the number of equivalence classes of the rules…
In this exploratory paper we introduce the problem of cognitive agents that learn how to modify their environment according to local sensing to reach a global goal. We concentrate on discrete dynamics (cellular automata) on a…
Controllability, one of the fundamental concepts in control theory, consists in guiding a system from an initial state to a desired one within a limited (and possibly minimum) time interval. When the objective is limited to a specific…
Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect…
This paper explores cellular automata (CA) constructed from Yang-Baxter maps over finite fields $F_{2^n}$. We define $R$-matrices using a map $f$ on $F_{2^n}$ and establish necessary and sufficient conditions for $f$ to satisfy the…
We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations…