Related papers: Ultimate Traces of Cellular Automata
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…
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…
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 extend a previously introduced semi-analytical representation of a decomposition of CA dynamics in arbitrary dimensions and neighborhood schemes via the use of certain universal maps in which CA rule vectors are derivable from 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…
The phase diagram of the coupled sine circle map lattice shows spatio-temporal intermittency of two distinct types: spatio-temporal intermittency of the directed percolation (DP) class, and spatial intermittency which does not belong to…
For any group $G$ and any set $A$, a cellular automaton (CA) is a transformation of the configuration space $A^G$ defined via a finite memory set and a local function. Let $\text{CA}(G;A)$ be the monoid of all CA over $A^G$. In this paper,…
In this dissertation, we study temporally stochasticity in cellular automata and the behavior of such cellular automata. The work also explores the computational ability of such cellular automaton that illustrates the computability of…
Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
We consider a left permutive cellular automaton Phi, with no memory and positive anticipation, defined on the space of all doubly infinite sequences with entries from a finite alphabet. For each such automaton that is not one-to-one, there…
A register automaton is a finite automaton with finitely many registers ranging from an infinite alphabet. Since the valuations of registers are infinite, there are infinitely many configurations. We describe a technique to classify…
We present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length $\varTheta(n^2)$, where…
Neural Cellular Automata (NCAs) are bio-inspired dynamical systems in which identical cells iteratively apply a learned local update rule to self-organize into complex patterns, exhibiting regeneration, robustness, and spontaneous dynamics.…
Since first introduced by John von Neumann, the notion of cellular automaton has grown into a key concept in computer science, physics and theoretical biology. In its classical setting, a cellular automaton is a transformation of the set of…
A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established. This result is found after proving a theorem on the…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial…
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…
Currently there is great interest in computational models consisting of underlying regular computational environments, and built on them distributed computational structures. Examples of such models are cellular automata, spatial…