Designing Complex Dynamics in Cellular Automata With Memory

Mart́ınez, Genaro J.; Adamatzky, Andrew; Alonso‐Sanz, Ramón

doi:10.1142/s0218127413300358

Cited by 26 publications

(29 citation statements)

References 62 publications

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“…With regards to memory effect in CA [10,11]. Recently, we have studied how a memory function helps to describe dynamics properties that are not evident at the first instance [29,28,39,38]. In present paper, the majority memory selected in ECA Rule 9 opens a new evolution rule ECAM φ R9maj:4 able to simulate solitons.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

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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“…A relatively new class of cellular automata approach is Elementary Cellular Automata with Memory (ECAM) [27,28]. The state of each cell is determined by the history of the cell using majority, minority or parity (XOR) rules.…”

Section: Cellular Automata Kernelmentioning

confidence: 99%

Symbolic Computation Using Cellular Automata-Based Hyperdimensional Computing

Yılmaz

2015

Neural Computation

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This letter introduces a novel framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation. A cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells, and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir. The proposed framework is shown to be capable of long-term memory, and it requires orders of magnitude less computation compared to echo state networks. As the focus of the letter, we suggest that binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way for concept building and symbolic processing. To demonstrate the capability of the proposed system, we make analogies directly on image data by asking, What is the automobile of air?

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“…The values of τ exceeding 10 do not change rules behaviour, i.e., not more changes are reported. An exhaustive description of this analysis is provided in [18]. Using this technique we classified ECA rules as follows.…”

Section: Ecam Classificationmentioning

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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Designing Complex Dynamics in Cellular Automata With Memory

Cited by 26 publications

References 62 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

Symbolic Computation Using Cellular Automata-Based Hyperdimensional Computing

On the Dynamics of Cellular Automata with Memory

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