scholarly journals Periodic Patterns in Orbits of Certain Linear Cellular Automata

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
André Barbé ◽  
Fritz Haeseler
Keyword(s):  
Cellular Automata ◽  
Finite Field ◽  
Cellular Automaton ◽  
Periodic Patterns ◽  
Periodic Behavior ◽  
Universal Behavior ◽  
International Audience

International audience We discuss certain linear cellular automata whose cells take values in a finite field. We investigate the periodic behavior of the verticals of an orbit of the cellular automaton and establish that there exists, depending on the characteristic of the field, a universal behavior for the evolution of periodic verticals.

scholarly journals Larger than Life: Digital Creatures in a Family of Two-Dimensional Cellular Automata

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Kellie M. Evans
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Nearest Neighbor ◽  
Two Dimensional ◽  
Game Of Life ◽  
Large Neighborhood ◽  
International Audience ◽  
Parameter Values

International audience We introduce the Larger than Life family of two-dimensional two-state cellular automata that generalize certain nearest neighbor outer totalistic cellular automaton rules to large neighborhoods. We describe linear and quadratic rescalings of John Conway's celebrated Game of Life to these large neighborhood cellular automaton rules and present corresponding generalizations of Life's famous gliders and spaceships. We show that, as is becoming well known for nearest neighbor cellular automaton rules, these ``digital creatures'' are ubiquitous for certain parameter values.

scholarly journals Representing Reversible Cellular Automata with Reversible Block Cellular Automata

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Jérôme Durand-Lose
Keyword(s):  
System Theory ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Linear Time ◽  
Fixed Size ◽  
Mathematical System ◽  
Reversible Cellular Automaton ◽  
International Audience ◽  
Infinite Lattices ◽  
Reversible Cellular Automata

International audience Cellular automata are mappings over infinite lattices such that each cell is updated according tothe states around it and a unique local function.Block permutations are mappings that generalize a given permutation of blocks (finite arrays of fixed size) to a given partition of the lattice in blocks.We prove that any d-dimensional reversible cellular automaton can be exp ressed as thecomposition of d+1 block permutations.We built a simulation in linear time of reversible cellular automata by reversible block cellular automata (also known as partitioning CA and CA with the Margolus neighborhood) which is valid for both finite and infinite configurations. This proves a 1990 conjecture by Toffoli and Margolus <i>(Physica D 45)</i> improved by Kari in 1996 <i>(Mathematical System Theory 29)</i>.

scholarly journals TOTALISTIC TWO-DIMENSIONAL CELLULAR AUTOMATA EXHIBITING GLOBAL PERIODIC BEHAVIOR

1999 ◽  
Vol 10 (06) ◽  
pp. 1017-1024 ◽  
Author(s):  
N. BOCCARA ◽  
M. ROGER
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Active Sites ◽  
Two Dimensional ◽  
Periodic Behavior ◽  
Stationary Density

We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an "average probabilistic totalistic rule" exhibiting the same periodic behavior.

Simulating Self-Regeneration and Self-Replication Processes Using Movable Cellular Automata with a Mutual Equilibrium Neighborhood

2020 ◽  
Vol 29 (4) ◽  
pp. 741-757
Author(s):  
Kateryna Hazdiuk ◽  
◽  
Volodymyr Zhikharevich ◽  
Serhiy Ostapov ◽  
◽  
...  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Three Dimensional ◽  
Computer Models ◽  
The Self ◽  
Model Construction ◽  
Natural Phenomena ◽  
Different Types ◽  
Movable Cellular Automata ◽  
Self Replication

This paper deals with the issue of model construction of the self-regeneration and self-replication processes using movable cellular automata (MCAs). The rules of cellular automaton (CA) interactions are found according to the concept of equilibrium neighborhood. The method is implemented by establishing these rules between different types of cellular automata (CAs). Several models for two- and three-dimensional cases are described, which depict both stable and unstable structures. As a result, computer models imitating such natural phenomena as self-replication and self-regeneration are obtained and graphically presented.

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

Simulation of microstructure evolution during recrystallization using a high resolution three dimensional cellular automaton

2004 ◽  
Vol 120 ◽  
pp. 225-230
Author(s):  
P. Mukhopadhyay ◽  
M. Loeck ◽  
G. Gottstein
Keyword(s):  
High Resolution ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Microstructure Evolution ◽  
Static Recrystallization ◽  
Three Dimensional ◽  
Computation Time ◽  
Recrystallization Process ◽  
Recovery Condition ◽  
Physically Based

A more refined 3D cellular Automata (CA) algorithm has been developed which has increased the resolution of the space and reduced the computation time and can take care of the complexity of recrystallization process through physically based solutions. This model includes recovery, condition for nucleation and orientation dependent variable nuclei growth as a process of primary static recrystallization. Incorporation of microchemistry effects makes this model suitable for simulating recrystallization behaviour in terms of texture, kinetics and microstructure of different alloys. The model is flexible to couple up with other simulation programs on a common database.

A Simple Three-States Cellular Automaton for Modelling Excitable Media

1998 ◽  
Vol 12 (05) ◽  
pp. 601-607 ◽  
Author(s):  
M. Andrecut
Keyword(s):  
Wave Propagation ◽  
Partial Differential Equations ◽  
Cellular Automata ◽  
Differential Equations ◽  
Cellular Automaton ◽  
Cellular Automaton Model ◽  
Excitable Media ◽  
Self Organization ◽  
Partial Differential ◽  
Bz Reaction

Wave propagation in excitable media provides an important example of spatiotemporal self-organization. The Belousov–Zhabotinsky (BZ) reaction and the impulse propagation along nerve axons are two well-known examples of this phenomenon. Excitable media have been modelled by continuous partial differential equations and by discrete cellular automata. Here we describe a simple three-states cellular automaton model based on the properties of excitation and recovery that are essential to excitable media. Our model is able to reproduce the dynamics of patterns observed in excitable media.

A Language Shift Simulation Based on Cellular Automata

2011 ◽  
pp. 136-151 ◽  
Author(s):  
Francesc S. Beltran ◽  
Salvador Herrando ◽  
Violant Estreder ◽  
Doris Ferreres ◽  
Marc-Antoni Adell ◽  
...  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Language Shift ◽  
Automata Theory ◽  
Theory Approach ◽  
Southern Europe ◽  
Social Phenomenon ◽  
Simulation Based ◽  
The World ◽  
Traditional Language

Language extinction is a widespread social phenomenon affecting several million people throughout the world today. By the end of this century, more than 5100 of the approximately 6000 languages currently spoken around the world will have disappeared. This is mainly because of language shifts, i.e., because a community of speakers stops using their traditional language and speaks a new one in all communication settings. In this study, the authors present the properties of a cellular automaton that incorporates some assumptions from the Gaelic-Arvanitika model of language shifts and the findings on the dynamics of social impacts in the field of social psychology. To assess the cellular automaton, the authors incorporate empirical data from Valencia (a region in Southern Europe), where Catalan speakers are tending to shift towards using Spanish. Running the automaton under different scenarios, the survival or extinction of Catalan in Valencia depends on individuals’ engagement with their language. The authors discuss how a cellular automata theory approach proves to be a useful tool for understanding the language shift.

scholarly journals Sequentializing cellular automata

2019 ◽  
Vol 19 (4) ◽  
pp. 759-772 ◽  
Author(s):  
Jarkko Kari ◽  
Ville Salo ◽  
Thomas Worsch
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Intermediate States ◽  
The Right

Abstract We study the problem of sequentializing a cellular automaton without introducing any intermediate states, and only performing reversible permutations on the tape. We give a decidable characterization of cellular automata which can be written as a single sweep of a bijective rule from left to right over an infinite tape. Such cellular automata are necessarily left-closing, and they move at least as much information to the left as they move information to the right.

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