Related papers: Fast Simulation of Cellular Automata by Self-Compo…
We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which ``particles'' embedded in…
In this work, we investigate the computational aspects of asynchronous cellular automata (ACAs), a modification of cellular automata in which cells update independently, following an asynchronous schedule. We introduce flip automata…
We present a 2-dimensional cellular automaton model for the simulation of pedestrian dynamics. The model is extremely efficient and allows simulations of large crowds faster than real time since it includes only nearest-neighbour…
Periodicity and relaxation are investigated for the trajectories of the states in one-dimensional finite cellular automata with rule-90 and 150. The time evolutions are described with matrices. Eigenvalue analysis is applied to clarify the…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
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…
Individual cellular automata rules are attractive models for a range of biological and physical self-assembling systems. While coexpression and coevolution are common in such systems, ensembles of cellular automata rules remain poorly…
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…
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 two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.
Various non-classical approaches of distributed information processing, such as neural networks, computation with Ising models, reservoir computing, vector symbolic architectures, and others, employ the principle of collective-state…
Cellular automata (CA) provide a minimal formalism for investigating how simple local interactions generate rich spatiotemporal behavior in domains as diverse as traffic flow, ecology, tissue morphogenesis and crystal growth. However,…
There exists algorithms to detect reversibility of cellular automaton (CA) for both finite and infinite lattices taking quadratic time. But, can we identify a $d$-state CA rule in constant time that is always reversible for every lattice…
In a recent paper Sutner proved that the first-order theory of the phase-space $\mathcal{S}_\mathcal{A}=(Q^\mathbb{Z}, \longrightarrow)$ of a one-dimensional cellular automaton $\mathcal{A}$ whose configurations are elements of…
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…
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…
It is well-known that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal's triangle modulo 2 generates a Sierpinski triangle. It has been shown that such patterns can occur when the alphabet is…
A number-conserving cellular automaton is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modelization of the physical…