How to make dull cellular automata complex by adding memory: Rule 126 case study

Mart́ınez, Genaro J.; Adamatzky, Andrew; Seck-Tuoh-Mora, Juan Carlos; Alonso‐Sanz, Ramón

doi:10.1002/cplx.20311

Cited by 29 publications

(18 citation statements)

References 34 publications

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“…In [29,38,39], we have demonstrated how ECA when enriched with memory with memory produces different dynamics. Here we will exploit this tool to get simple solitonic reactions.…”

Section: Solitons In Ecammentioning

confidence: 98%

On Soliton Collisions between Localizations in Complex Elementary Cellular Automata: Rules 54 and 110 and Beyond

Mart́ınez¹,

Adamatzky²,

Chen³

et al. 2012

ComplexSystems

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In this paper we present a single-soliton two-component cellular automata (CA) model of waves as mobile self-localizations, also known as: particles, waves, or gliders; and its version with memory. The model is based on coding sets of strings where each chain represents a unique mobile self-localization. We will discuss briefly the original soliton models in CA proposed with filter automata, followed by solutions in elementary CA (ECA) domain with the famous universal ECA Rule 110, and reporting a number of new solitonic collisions in ECA Rule 54. A mobile self-localization in this study is equivalent a single soliton because the collisions of these mobile self-localizations studied in this paper satisfies the property of solitonic collisions. We also present a specific ECA with memory (ECAM), the ECAM Rule φR9maj:4, that displays single-soliton solutions from any initial codification (including random initial conditions) for a kind of mobile self-localization because such automaton is able to adjust any initial condition to soliton structures.

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“…In [29,38,39], we have demonstrated how ECA when enriched with memory with memory produces different dynamics. Here we will exploit this tool to get simple solitonic reactions.…”

Section: Solitons In Ecammentioning

confidence: 98%

On Soliton Collisions between Localizations in Complex Elementary Cellular Automata: Rules 54 and 110 and Beyond

Mart́ınez¹,

Adamatzky²,

Chen³

et al. 2012

ComplexSystems

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“…Here we consider a particular case to illustrate the effect of memory, deriving in complex dynamics from a chaotic rule [23]. We deal with the chaotic ECA (class III) rule 126.…”

Section: Rule 126 With Memory: Case Study Of Complexitymentioning

confidence: 99%

“…We can deduce from previous analysis that ECA rule 126 could contain another kind of interesting information. Selecting a kind of memory we will see that particularly ECAM φ R126maj:4 displays a large number of glider guns emerging from random initial conditions, and emergence of a number of non-trivial patterns colliding constantly [23].…”

Section: Rule 126 With Memory: Case Study Of Complexitymentioning

confidence: 99%

On the Dynamics of Cellular Automata with Memory

Mart́ınez

Adamatzky

Alonso‐Sanz

2015

Fundamenta Informaticae

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Elementary cellular automata (ECA) are linear arrays of finite-state machines (cells) which take binary states, and update their states simultaneously depending on states of their closest neighbours. We design and study ECA with memory (ECAM), where every cell remembers its states during some fixed period of evolution. We characterize complexity of ECAM in a case study of rule 126, and then provide detailed behavioural classification of ECAM. We show that by enriching ECA with memory we can achieve transitions between the classes of behavioural complexity. We also show that memory helps to 'discover' hidden information and behaviour on trivial (uniform, periodic), and non-trivial (chaotic, complex) dynamical systems.

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“…Some CA evolutions present dominant periodic backgrounds, sometimes called ethers, as in the famous universal elementary CA (ECA) rule 110 [8,29]. Other, more exotic CAs (with respect to alphabet, neighborhood, and dimensions) can be studied in DDLab; they may evolve with two, three, four, or more periodic or chaotic backgrounds at the same time, with gliders and other complex patterns emerging during their histories [6,16,22,30]. Filters have been demonstrated to be useful to explore and clarify particles (gliders or mobile self-localizations) and collisions between them in unconventional computing models [14][15][16].…”

mentioning

confidence: 99%

“…This could easily be done by including information from historical time steps (which DDLab already records for other functions) when calculating the next time step. CAs with memory have been demonstrated to be simple, interesting, and powerful in exploring other new domains of complex evolution rules and computable systems [14,16,17].…”

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confidence: 99%

Exploring Discrete Dynamics.Andrew Wuensche. (2011, Luniver Press.) xxxvii + 498 pages, 290 figures, 31 tables.

Mart́ınez

2012

Artificial Life

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Exploring Discrete Dynamics. Andrew Wuensche. (2011, Luniver Press.) xxxvii + 498 pages, 290 figures, 31 tables.Exploring Discrete Dynamics is a very extended computational and analytic exploration of discrete dynamical systems. The book makes a summary of more than 19 years of results, programming, and research by Andrew Wuensche.In 1992, at the Santa Fe Institute, Wuensche together with Mike Lesser published the celebrated book in cellular automata theory The Global Dynamics of Cellular Automata [26]. This book introduced a reverse algorithm for cellular automata, and presented an atlas of basin of attraction fields computed by means of the algorithm. Motivated by these results and Kauffmanʼs model of genetic regulatory networks [12], Wuensche subsequently developed new algorithms for random Boolean networks and discrete dynamical networks in general. His achievements have had a great influence on outstanding researchers such as Stuart Kauffman [12], Harold V. McIntosh [18], Andrew Adamatzky [1], and Christopher Langton [26], among many others; and hundreds of references in books and research articles.These results have been obtained mainly by making use of his popular open source software DDLab (Discrete Dynamics Lab, http://www.ddlab.org/), which is widely used in the scientific community and offers free access to software, code, and manual. Wuenscheʼs latest book, Exploring Discrete Dynamics, presents a very extensive description of the current features of DDLab. Successive chapters describe, in detail and in depth, every function of this tool, illustrated with numerous examples from his research.Analyses concentrate mainly on four systems of increasing generality: cellular automata (CAs), random Boolean networks (RBNs), discrete dynamical networks (DDNs), and random maps. Consequently, in this book we have a ramification that connects and relates concepts naturally derived from these main subjects: reverse algorithms, rule space, state space, basins of attraction, DDLab software is unique in its ability to study and classify discrete dynamical systems, analyze and unravel networks with the network graph, create flexible simulations where parameters can be changed on the fly, and generate basins of attraction and subtrees. In DDLab we can experiment with mutations, calculate preimages (or ancestors [10, 23]), and analyze state space configurations iterating for unlimited spans of time, including simulations in one, two, and three dimensions. In the state space implementation, we can calculate the changing input entropy and pattern density, which helps us to understand the properties of dynamical systems-applied in particular to automatically categorize CA rule space between order, complexity, and chaos. The static Z parameter, based on just the rule table, also categorizes CA rule space by predicting the indegree in subtrees to identify maximum chaos-this is applied for a method of encryption [34].An interesting point in the book is the incorporation of a jump graph of the basin of attraction field (see p. ...

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How to make dull cellular automata complex by adding memory: Rule 126 case study

Cited by 29 publications

References 34 publications

On Soliton Collisions between Localizations in Complex Elementary Cellular Automata: Rules 54 and 110 and Beyond

On Soliton Collisions between Localizations in Complex Elementary Cellular Automata: Rules 54 and 110 and Beyond

On the Dynamics of Cellular Automata with Memory

Exploring Discrete Dynamics.Andrew Wuensche. (2011, Luniver Press.) xxxvii + 498 pages, 290 figures, 31 tables.

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