Related papers: Flexible Time and the Evolution of One-Dimensional…
Cellular automata are computers, similar to Turing machines. The main difference is that Turing machines use a one-dimensional tape, whereas cellular automata use a two-dimensional grid. The best-known cellular automaton is the Game of…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
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…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
Periodicity and relaxation are investigated for the trajectories of the states in cylindrical linear cellular automata. The time evolutions are described with matrices. The eigenvalue analysis is applied to obtain the maximum values of…
A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
In this work, the one-dimensional Cellular Automaton is extended to one that involves two sets of symbols and two global rules. As a main result, the Extended Curtis-Hedlund-Lyndon Theorem is demonstrated. Such constructions can be useful…
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 automaton (CA) approach is an important theoretical framework for studying complex system behavior and has been widely applied in various research field. CA traffic flow models have the advantage of flexible evolution rules and…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…
We derive a set of algorithms for simulating the diffusion-limited growth of faceted crystals using local cellular automata. This technique has been shown to work well in reproducing realistic crystal morphologies, and the present work…
The cellular automata discrete dynamical system is considered as the two-stage process: the majority rule for the change in the automata state and the rule for the change in topological relations between automata. The influence of changing…
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…
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…