Automatic Texture Based Classification of the Dynamics of One-Dimensional Binary Cellular Automata

2019 ◽  
Vol 8 (4) ◽  
pp. 41-61
Author(s):  
Marcelo Arbori Nogueira ◽  
Pedro Paulo Balbi de Oliveira
Keyword(s):  
Cellular Automata ◽  
Dynamic Behavior ◽  
Temporal Evolution ◽  
Computational Cost ◽  
Great Variability ◽  
Texture Descriptor ◽  
One Dimensional ◽  
Binary Images ◽  
Elementary Cellular Automata

Cellular automata present great variability in their temporal evolutions due to the number of rules and initial configurations. The possibility of automatically classifying its dynamic behavior would be of great value when studying properties of its dynamics. By counting on elementary cellular automata, and considering its temporal evolution as binary images, the authors created a texture descriptor of the images - based on the neighborhood configurations of the cells in temporal evolutions - so that it could be associated to each dynamic behavior class, following the scheme of Wolfram's classic classification. It was then possible to predict the class of rules of a temporal evolution of an elementary rule in a more effective way than others in the literature in terms of precision and computational cost. By applying the classifier to the larger neighborhood space containing 4 cells, accuracy decreased to just over 70%. However, the classifier is still able to provide some information about the dynamics of an unknown larger space with reduced computational cost.

Definition and Application of a Five-Parameter Characterization of One-Dimensional Cellular Automata Rule Space

2001 ◽  
Vol 7 (3) ◽  
pp. 277-301 ◽  
Author(s):  
Gina M. B. Oliveira ◽  
Pedro P. B. de Oliveira ◽  
Nizam Omar
Keyword(s):  
Phase Transition ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Dynamic Behavior ◽  
Discrete Dynamical Systems ◽  
Transition Diagram ◽  
One Dimensional ◽  
Rule Space ◽  
Spatially Extended

Cellular automata (CA) are important as prototypical, spatially extended, discrete dynamical systems. Because the problem of forecasting dynamic behavior of CA is undecidable, various parameter-based approximations have been developed to address the problem. Out of the analysis of the most important parameters available to this end we proposed some guidelines that should be followed when defining a parameter of that kind. Based upon the guidelines, new parameters were proposed and a set of five parameters was selected; two of them were drawn from the literature and three are new ones, defined here. This article presents all of them and makes their qualities evident. Then, two results are described, related to the use of the parameter set in the Elementary Rule Space: a phase transition diagram, and some general heuristics for forecasting the dynamics of one-dimensional CA. Finally, as an example of the application of the selected parameters in high cardinality spaces, results are presented from experiments involving the evolution of radius-3 CA in the Density Classification Task, and radius-2 CA in the Synchronization Task.

Cellular Automata

2017 ◽  
Vol 29 (1) ◽  
pp. 42-50 ◽  
Author(s):  
Rupali Bhardwaj ◽  
Anil Upadhyay
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Empirical Study ◽  
Time Evolution ◽  
Discrete Dynamical Systems ◽  
The State ◽  
Dimensional Lattice ◽  
Elementary Cellular Automata

Cellular automata (CA) are discrete dynamical systems consist of a regular finite grid of cell; each cell encapsulating an equal portion of the state, and arranged spatially in a regular fashion to form an n-dimensional lattice. A cellular automata is like computers, data represented by initial configurations which is processed by time evolution to produce output. This paper is an empirical study of elementary cellular automata which includes concepts of rule equivalence, evolution of cellular automata and classification of cellular automata. In addition, explanation of behaviour of cellular automata is revealed through example.

Topological Conjugacy Classification of Elementary Cellular Automata with Majority Memory

2017 ◽  
Vol 27 (14) ◽  
pp. 1750217 ◽  
Author(s):  
Haiyun Xu ◽  
Fangyue Chen ◽  
Weifeng Jin
Keyword(s):  
Cellular Automata ◽  
Vector Space ◽  
Symbolic Dynamics ◽  
Continuous Functions ◽  
Equivalence Classes ◽  
Topological Conjugacy ◽  
Symbolic Sequence ◽  
And Topology ◽  
Elementary Cellular Automata

The topological conjugacy classification of elementary cellular automata with majority memory (ECAMs) is studied under the framework of symbolic dynamics. In the light of the conventional symbolic sequence space, the compact symbolic vector space is identified with a feasible metric and topology. A slight change is introduced to present that all global maps of ECAMs are continuous functions, thereafter generating the compact dynamical systems. By exploiting two fundamental homeomorphisms in symbolic vector space, all ECAMs are furthermore grouped into 88 equivalence classes in the sense that different mappings in the same global equivalence are mutually topologically conjugate.

scholarly journals EXPRESSIVENESS OF ELEMENTARY CELLULAR AUTOMATA

2013 ◽  
Vol 24 (03) ◽  
pp. 1350010 ◽  
Author(s):  
MARKUS REDEKER ◽  
ANDREW ADAMATZKY ◽  
GENARO J. MARTÍNEZ
Keyword(s):  
Cellular Automata ◽  
Biological Systems ◽  
Biologically Inspired ◽  
One Dimensional ◽  
Elementary Cellular Automata

We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically inspired parameters for biodiversity are applied to the configurations of cellular automata. This paper contains a survey of the Elementary Cellular Automata in terms of their expressiveness and an evaluation whether expressiveness is a meaningful term in the context of simulated biology.

scholarly journals Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental Study

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 209
Author(s):  
Qin Lei ◽  
Jia Lee ◽  
Xin Huang ◽  
Shuji Kawasaki
Keyword(s):  
Cellular Automata ◽  
Complex Systems ◽  
Complete Classification ◽  
Asymptotic Density ◽  
Elementary Cellular Automata ◽  
Local Patterns ◽  
One Step ◽  
Pattern Distribution ◽  
High Uncertainty

Classification of asynchronous elementary cellular automata (AECAs) was explored in the first place by Fates et al. (Complex Systems, 2004) who employed the asymptotic density of cells as a key metric to measure their robustness to stochastic transitions. Unfortunately, the asymptotic density seems unable to distinguish the robustnesses of all AECAs. In this paper, we put forward a method that goes one step further via adopting a metric entropy (Martin, Complex Systems, 2000), with the aim of measuring the asymptotic mean entropy of local pattern distribution in the cell space of any AECA. Numerical experiments demonstrate that such an entropy-based measure can actually facilitate a complete classification of the robustnesses of all AECA models, even when all local patterns are restricted to length 1. To gain more insights into the complexity concerning the forward evolution of all AECAs, we consider another entropy defined in the form of Kolmogorov–Sinai entropy and conduct preliminary experiments on classifying their uncertainties measured in terms of the proposed entropy. The results reveal that AECAs with low uncertainty tend to converge remarkably faster than models with high uncertainty.

Formal Logic of Cellular Automata

2021 ◽  
Vol 30 (2) ◽  
pp. 187-203
Author(s):  
Sukanta Das ◽  
◽  
Mihir K. Chakraborty ◽  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Formal Logic ◽  
One Dimensional ◽  
Elementary Cellular Automata ◽  
Binary Strings

This paper develops a formal logic, named L CA , targeting modeling of one-dimensional binary cellular automata. We first develop the syntax of L CA , then give semantics to L CA in the domain of all binary strings. Then the elementary cellular automata and four-neighborhood binary cellular automata are shown as models of the logic. These instances point out that there are other models of L CA . Finally it is proved that any one-dimensional binary cellular automaton is a model of the proposed logic.

Fundamental of Cellular Automata Theory

2017 ◽  
pp. 26-51
Keyword(s):  
Cellular Automata ◽  
Automata Theory ◽  
Linear Feedback ◽  
Random Number Generators ◽  
Von Neumann ◽  
One Dimensional ◽  
Asynchronous Cellular Automata ◽  
Local Functions ◽  
Definition Of

In this chapter, the author reviews the main historical aspects of the development of cellular automata. The basic structures of cellular automata are described. The classification of cellular automata is considered. A definition of a one-dimensional cellular automaton is given and the basic rules for one-dimensional cellular automata are described that allow the implementation of pseudo-random number generators. One-dimensional cellular automata with shift registers with linear feedback are compared. Synchronous two-dimensional cellular automata are considered, as well as their behavior for various using local functions. An analysis of the functioning of synchronous cellular automata for the neighborhoods of von Neumann and Moore is carried out. A lot of attention is paid to asynchronous cellular automata. The necessary definitions and rules for the behavior of asynchronous cellular automata are given.

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