Cellular Automata with Memory

Alonso‐Sanz, Ramón

doi:10.1007/978-0-387-30440-3_55

Cited by 22 publications

(27 citation statements)

References 43 publications

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“…CA with memory are an extension of CA in such a way that every cell x i is allowed to remember its states during some fixed period of its evolution. CA with memory have been proposed originally by Alonso-Sanz in [3,4,5,6]. Hence we implement a memory function φ, as follows: s…”

Section: Elementary Cellular Automata With Memory (Ecam)mentioning

confidence: 99%

“…Thus in CA with memory, while the mapping ϕ remains unaltered, historic memory of all past iterations is retained by featuring each cell as a summary of its past states from φ. We can say that cells canalise memory to the map ϕ [4,5].…”

Section: Elementary Cellular Automata With Memory (Ecam)mentioning

confidence: 99%

“…. ., etc [5,6]. Evolution rules representation for ECAM in this paper is given in [16,17,19] as follows: φ CARm:τ where CAR is the decimal notation of a particular ECA rule and m is the kind of memory used with a specific value of τ .…”

Section: Elementary Cellular Automata With Memory (Ecam)mentioning

confidence: 99%

“…CA with memory opened a new family of evolution rules with different and interesting dynamics [5,6]. We explore three types of memory: minority, majority, and parity.…”

Section: Dynamics Emerging In Eca Rule 126 With Memorymentioning

confidence: 99%

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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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Section: Elementary Cellular Automata With Memory (Ecam)mentioning

confidence: 99%

Section: Elementary Cellular Automata With Memory (Ecam)mentioning

confidence: 99%

Section: Elementary Cellular Automata With Memory (Ecam)mentioning

confidence: 99%

“…CA with memory opened a new family of evolution rules with different and interesting dynamics [5,6]. We explore three types of memory: minority, majority, and parity.…”

Section: Dynamics Emerging In Eca Rule 126 With Memorymentioning

confidence: 99%

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On the Dynamics of Cellular Automata with Memory

Mart́ınez

Adamatzky

Alonso‐Sanz

2015

Fundamenta Informaticae

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“…There will always be extra functions in any wish list (and users can themselves revise the open source code). My suggestion is to consider another variation of the CA, the CA with memory (see [2,3]). 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.…”

mentioning

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

et al. 2010

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Using Rule 126 elementary cellular automaton (ECA) we demonstrate that a chaotic discrete system -when enriched with memory -hence exhibits complex dynamics where such space exploits on an ample universe of periodic patterns induced from original information of the ahistorical system. First we analyse classic ECA Rule 126 to identify basic characteristics with mean field theory, basins, and de Bruijn diagrams. In order to derive this complex dynamics, we use a kind of memory on Rule 126; from here interactions between gliders are studied for detecting stationary patterns, glider guns and simulating specific simple computable functions produced by glider collisions.

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Cellular Automata with Memory

Cited by 22 publications

References 43 publications

On the Dynamics of Cellular Automata with Memory

On the Dynamics of Cellular Automata with Memory

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

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

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