Discrete systems with memory

by Alonso Sanz, Ramón

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Title Statements

Full title :Discrete systems with memory / Ramon Alonso-Sanz.

Summary

Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions. It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian : only the actual configuration is taken into account to generate the next one. Generalizing the conventional view on spatially extended discrete dynamical systems evolution by allowing cells (or nodes) to be featured by some trait state computed as a function of its own previous state-values, the transition maps of the classical systems are kept unaltered, so that the effect of memory can be easily traced. The book demonstrates that discrete dynamical systems with memory are not only priceless tools for modeling natural phenomena but unique mathematical and aesthetic objects.

Edition Statements

Publication Date:©2011.

Publication Statements

Publisher(s):World Scientific
Place of Publication:Singapore
Language:eng
Publication Date:©2011.

Notes

Titre de l'écran-titre (visionné le 02 mai 2012).

TRAITEMENT SOMMAIRE.

The Physical Object

Description:1 online resource.

Edition Identifiers

oclc:ocn840864078
LC Classification:QA267.5.C45
Dewey Decimal:511.3/5

1. Cellular automata and memory. 1.1. Cellular automata. 1.2. Memory -- 2. Average type memory. 2.1. Average memory. 2.2. Two-dimensional lattices. 2.3. One-dimensional layers -- 3. Other memories. 3.1. Average-like memory. 3.2. Limited trailing memory. 3.3. Majority of the last three state memory. 3.4. Elementary rules as memory. 3.5. Minimal memory -- 4. Asynchrony and probabilistic rules. 4.1. Asynchrony. 4.2. Probabilistic rules -- 5. Cycles and random sequences. 5.1. Cycles. 5.2. Random number generation by CA -- 6. Three state automata. 6.1. Totalistic rules. 6.2. Excitable systems -- 7. Reversible dynamics. 7.1. Characterization. 7.2. Reversible rules with memory -- 8. Block cellular automata. 8.1. Characterization. 8.2. Density classification task -- 9. Structurally dynamic systems. 9.1. Introduction. 9.2. SDCA with memory -- 10. Boolean networks. 10.1. Automata on networks. 10.2. Boolean networks. 10.3. Automata on proximity graphs -- 11. Coupled layers. 11.1. Coupled cellular automata. 11.2. Coupled Boolean networks -- 12. Continuous state variable. 12.1. Continuous-valued automata. 12.2. Finite difference equations. 12.3. Plane curves. 12.4. Stochastic processes -- 13. …

Subjects

Automates cellulaires -- Modèles mathém… Cellular automata -- Mathematical models Discrete-time systems -- Mathematical m… Dynamics Dynamique e-books Livres électroniques Livres numériques Systèmes échantillonnés -- Modèles math…