Complete sets of initial vectors for pattern growth with elementary cellular automata

Freire, Joana G.; Brison, Owen J.; Gallas, Jason A. C.

doi:10.1016/j.cpc.2009.12.007

Cited by 5 publications

(4 citation statements)

References 35 publications

(52 reference statements)

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“…As well, Freire et. al developed an approach to select specific sets of vectors, initial configurations, that determine development of gliders and localised patterns [18,19]. Finally, the de Bruijn diagrams is a time-tested and reliable tool to classify sets of periodic structures or gliders using exhaustive approach [40,41].…”

Section: Discussionmentioning

confidence: 99%

Cellular Automaton Supercolliders

Mart́ınez

Adamatzky

Stephens

et al. 2011

Int. J. Mod. Phys. C

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Gliders in one-dimensional cellular automata are compact groups of nonquiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton 'cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems.

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Section: Discussionmentioning

confidence: 99%

Cellular Automaton Supercolliders

Mart́ınez

Adamatzky

Stephens

et al. 2011

Int. J. Mod. Phys. C

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“…After predicting how many they are and thereby restricting the universe to be investigated, the next important question is to have an efficient algorithm to compute without repetitions the minimal set of initial conditions that need to be tested. Such an algorithm now exists and is reported elsewhere [22]. The formula for n(k) provides an accurate estimate of the computational complexity involved in application of the spacewise algorithm to obtain exhaustive answers concerning the spatio-temporal organization of cellular automaton models of, e.g., computer networks [23][24][25][26].…”

Section: Discussionmentioning

confidence: 99%

Exact quantification of the complexity of spacewise pattern growth in cellular automata

Freire

Brison

Gallas

2009

J. Phys. A: Math. Theor.

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We analyze the two possible ways of simulating complex systems with cellular automata: by using the familiar timewise updating or by using the complementary spacewise updating. Both updating algorithms operate on identical sets of initial conditions defining the state of the automaton. While timewise growth generally probes just vanishingly small sets of initial conditions producing statistical samples of the asymptotic attractors, spacewise growth operates with much restricted sets which allow one to simulate them all, exhaustively. Our main result is the derivation of an exact analytical formula to quantify precisely one of the two sources of algorithmic complexity of spacewise detection of the complete set of attractors for elementary 1D cellular automata with generic non-periodic architectures of any arbitrary size. The formula gives the total number of initial conditions that need to be investigated to locate rigorously all possible patterns for any given rule. As simple applications, we illustrate how this knowledge may be used (i) to uncover missing patterns in previous classifications in the literature and (ii) to obtain surprisingly novel patterns that are totally unreachable with the time-honored technique of artificially imposing spatially periodic boundary conditions.

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“…C ellular automata have been applied over time to model dynamical systems occurring in all range of organized behavior, such as statistical physics, biology, medicine, ecology, and socioeconomic interaction (Aristotelous and Durrett, 2014;Brännström and Sumpter, 2005;Clifford and Sudbury, 1973;Freire et al, 2010;Griffeath and Moore, 2002;Levy and Requeijo, 2008;Nguyen et al, 2005;O'Sullivan and Perry, 2009). They are a class of interacting particle systems, a paradigm for large dynamical systems comprising numerous particles that are allowed to interact on certain local neighborhood rules.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Cellular Automata

2018

Emergence, Complexity and Computation

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The Emergence, Complexity and Computation (ECC) series publishes new developments, advancements and selected topics in the fields of complexity, computation and emergence. The series focuses on all aspects of reality-based computation approaches from an interdisciplinary point of view especially from applied sciences, biology, physics, or chemistry. It presents new ideas and interdisciplinary insight on the mutual intersection of subareas of computation, complexity and emergence and its impact and limits to any computing based on physical limits (thermodynamic and quantum limits, Bremermann's limit, Seth Lloyd limits…) as well as algorithmic limits (Gödel's proof and its impact on calculation, algorithmic complexity, the Chaitin's Omega number and Kolmogorov complexity, non-traditional calculations like Turing machine process and its consequences,…) and limitations arising in artificial intelligence field. The topics are (but not limited to) membrane computing, DNA computing, immune computing, quantum computing, swarm computing, analogic computing, chaos computing and computing on the edge of chaos, computational aspects of dynamics of complex systems (systems with self-organization, multiagent systems, cellular automata, artificial life,…), emergence of complex systems and its computational aspects, and agent based computation. The main aim of this series it to discuss the above mentioned topics from an interdisciplinary point of view and present new ideas coming from mutual intersection of classical as well as modern methods of computation. Within the scope of the series are monographs, lecture notes, selected contributions from specialized conferences and workshops, special contribution from international experts. This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. PrefaceProbabilistic cellular automata (PCA) are interacting discrete stochastic dynamical sy...

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Complete sets of initial vectors for pattern growth with elementary cellular automata

Cited by 5 publications

References 35 publications

Cellular Automaton Supercolliders

Cellular Automaton Supercolliders

Exact quantification of the complexity of spacewise pattern growth in cellular automata

Probabilistic Cellular Automata

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