Related papers: Continuum versus Discrete: A Physically Interpreta…
To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to…
A cellular automaton named Rule 184++C is proposed as a meta-model to investigate the flow of various complex particles. In this model, unlike the granular pipe flow and the traffic flow, not only the free-jam phase transition but also the…
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…
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
One of the most important problems in contemporary science, and especially in biology, is to reveal mechanisms of pattern formation. On the level of biological tissues, patterns form due to interactions between cells. These interactions can…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
This article surveys some theoretical aspects of Cellular Automata (CAs) research. In particular, we discuss on maximal length CA. An n-cell CA is a maximal length CA, if all the configurations except one form a single cycle. There is a…
We prove the existence of a semilinear representation of Cellular Automata (CA) with the introduction of multiple convolution kernels. Examples of the technique are presented for rules akin to the "edge-of-chaos" including the Turing…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
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…
When investigating theories at the tiniest conceivable scales in nature, almost all researchers today revert to the quantum language, accepting the verdict from the Copenhagen doctrine that the only way to describe what is going on will…
Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
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…
We construct a two dimensional Cellular Automata based model for the description of pedestrian dynamics. Wide range of complicated pattern formation phenomena in pedestrian dynamics are described in the model, e.g. lane formation, jams in a…
Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by…