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We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as…
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…
Previous work introduced a lower-dimensional numerical model for the geometric nonlinear simulation and optimization of compliant pressure actuated cellular structures. This model takes into account hinge eccentricities as well as…
Noise in the local transition function is compared to fluctuations in the updating times of the cells. Obtained results are shown to be quite different in both cases. In this extended abstract we briefly explain the problem and present…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the r esult could actually make sense physically, as a valid quantum evolution; but…
We analyze a stochastic 5-neighbor cellular automaton with several conserved quantities, including the particle density. By examining the eigenvalue problem of the associated transition matrix, we derive an explicit formula for the…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
For a group $G$ and a finite set $A$, a cellular automaton is a transformation of the configuration space $A^G$ defined via a finite neighborhood and a local map. Although neighborhoods are not unique, every CA admits a unique minimal…
The quantum cellular automata (QCA) effect is a transition in which multiple electron move coordinately by Coulomb interactions and observed in multiple quantum dots. This effect will be useful for realizing and improving quantum cellular…
Models of areas of physics in terms of cellular automata have become increasingly popular. Cellular automata (CAs) support the modeling of systems with discrete state component values and enforce the comprehensive specification of the…
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular…
A recently introduced cellular automaton model for the description of traffic flow is investigated. It generalises asymmetric exclusion models which have attracted a lot of interest in the past. We calculate the so-called fundamental…
We present some computer simulations run on a stochastic CA (cellular automaton). The CA simulates a gas of particles which are in a channel, the interval $[1,L]$ in $\mathbb Z$, but also in "reservoirs" $\mathcal R_1$ and $\mathcal R_2$.…
We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of…
Triangles are everywhere in the virtual world. The surface of nearly every graphical object is saved as a triangular mesh on a computer. Light effects and movements of virtual objects are computed on the basis of triangulations. Besides…
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…
A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the…
Cellular Automata (CA) theory is a discrete model that represents the state of each of its cells from a finite set of possible values which evolve in time according to a pre-defined set of transition rules. CA have been applied to a number…