Related papers: Logic gates and complex dynamics in a hexagonal ce…
Higher-order cellular automata (HOCA) are a variant of cellular automata (CA) used in many applications (ranging, for instance, from the design of secret sharing schemes to data compression and image processing), and in which the global…
This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…
In cellular automata models a glider gun is an oscillating pattern of non-quiescent states that periodically emits traveling localizations (gliders). The glider streams can be combined to construct functionally complete systems of logical…
We investigate the critical behaviour of a probabilistic mixture of cellular automata (CA) rules 182 and 200 (in Wolfram's enumeration scheme) by mean-field analysis and Monte Carlo simulations. We found that as we switch off one CA and…
We study intrinsic simulations between cellular automata and introduce a new necessary condition for a CA to simulate another one. Although expressed for general CA, this condition is targeted towards surjective CA and especially linear…
We study a quantum cellular automaton (QCA) whose time-evolution is defined from global transition function of classical cellular automata (CA). In order to investigate natural transformations from CA to QCA, the present QCA includes CA…
We study charge fluctuations of a family of stochastic charged cellular automata away from the deterministic single-file limit and obtain the exact typical charge probability distributions, known to be anomalous, using hydrodynamics. The…
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
Since their inception at {\it Macy conferences} in later 1940s complex systems remain the most controversial topic of inter-disciplinary sciences. The term `complex system' is the most vague and liberally used scientific term. Using…
We reproduce apparently complex cellular automaton behaviour with simple partial differential equations as developed in (Keane 09). Our PDE model easily explains behaviour observed in selected scenarios of the cellular automaton wargame…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
Gravitational clustering of a random distribution of point masses is dominated by the effective short-range interactions due to large-scale isotropy. We introduce a one-dimensional cellular automaton to reproduce this effect in the most…
Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…
Local interactions among biomolecules, and the role played by their environment, have gained increasing attention in modelling biochemical reactions. By defining the automaton of molecular perceptions, we explore an agent-based…
We present a derivation of a formula that gives dynamics of an integrable cellular automaton associated with crystal bases. This automaton is related to type D affine Lie algebra and contains usual box-ball systems as a special case. The…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is pi-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the…
We introduce our GraftalLace Cellular Automaton in short GLCA which is a new one-dimensional cellular automaton on the regular square lattice. It makes a monochromatic infinite directed graph otherwise an octal number triangle or number…
Partitioned cellular automata are known to be an useful tool to simulate linear and nonlinear problems in physics, specially because they allow for a straightforward way to define conserved quantities and reversible dynamics. Here we show…
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…