scholarly journals Classification of Elementary Cellular Automata Up to Topological Conjugacy

2015 ◽  
pp. 99-112 ◽  
Author(s):  
Jeremias Epperlein
Keyword(s):  
Cellular Automata ◽  
Topological Conjugacy ◽  
Elementary Cellular Automata

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.

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.

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.

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.

Elementary cellular automata and self-referential paradoxes

2020 ◽  
Vol 30 (3) ◽  
pp. 745-763
Author(s):  
MING HSIUNG
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Fixed Points ◽  
Evolution Process ◽  
New Classification ◽  
Revision Process ◽  
Elementary Cellular Automata ◽  
Elementary Cellular Automaton

Abstract We associate an elementary cellular automaton with a set of self-referential sentences, whose revision process is exactly the evolution process of that automaton. A simple but useful result of this connection is that a set of self-referential sentences is paradoxical, iff (the evolution process for) the cellular automaton in question has no fixed points. We sort out several distinct kinds of paradoxes by the existence and features of the fixed points of their corresponding automata. They are finite homogeneous paradoxes and infinite homogeneous paradoxes. In some weaker sense, we will also introduce no-no-sort paradoxes and virtual paradoxes. The introduction of these paradoxes, in turn, leads to a new classification of the cellular automata.

scholarly journals An Information-Based Classification of Elementary Cellular Automata

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Enrico Borriello ◽  
Sara Imari Walker
Keyword(s):  
Cellular Automata ◽  
Classification Scheme ◽  
Initial Conditions ◽  
Coarse Graining ◽  
Transfer Entropy ◽  
Initial State ◽  
Elementary Cellular Automata ◽  
State Transfer ◽  
Sensitivity To Initial Conditions

We propose a novel, information-based classification of elementary cellular automata. The classification scheme proposed circumvents the problems associated with isolating whether complexity is in fact intrinsic to a dynamical rule, or if it arises merely as a product of a complex initial state. Transfer entropy variations processed by cellular automata split the 256 elementary rules into three information classes, based on sensitivity to initial conditions. These classes form a hierarchy such that coarse-graining transitions observed among elementary rules predominately occur within each information-based class or, much more rarely, down the hierarchy.

The Fixed String of Elementary Cellular Automata

2010 ◽  
Vol 19 (3) ◽  
pp. 243-262
Author(s):  
Jiang Zhisong ◽  
◽  
Qin Dakang ◽  
Keyword(s):  
Cellular Automata ◽  
Elementary Cellular Automata
Sign in / Sign up

Export Citation Format

Share Document