Elementary Cellular Automata with Memory of Delay Type

Alonso‐Sanz, Ramón

doi:10.1007/978-3-642-40867-0_5

Cited by 5 publications

(9 citation statements)

References 10 publications

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“…For details please see [Wuensche & Lesser, 1992]. full-asymmetric: 10,11,14,15,24,25,28,29,42,43,46,57,60,138,142,152,156,170,184. strong: 10, 11, 15, 24, 25, 42, 46, 57, 138, 152, 170, 184. moderate: 14, 28, 29, 43, 142, 156. weak: 60.…”

Section: Wuensche's Equivalences (1992)mentioning

confidence: 99%

“…For details please see [Ninagawa, 2008]. 3,6,7,9,10,11,14,15,18,22,24,25,26,27,30,34,35,37,38,41,42,43,45,46,54,56,57,58,60,62,74,106,110,122,126,130,134,138,142,146,152,154,162,170,184.…”

Section: Wuensche's Equivalences (1992)mentioning

confidence: 99%

“…In this study we have implemented an explicit dependence in the dynamics of the past states in the manner: first summary then rule. But the order summary-rule may be inverted, i.e., the rule is first applied and a summary is then presented as new state (for details see [Alonso-Sanz, 2013]. This alternative memory implemention enriches the potential use of memory in discrete systems as a tool for modeling, and, again, in our opinion deserves attention on its own.…”

Section: Final Remarksmentioning

confidence: 99%

See 2 more Smart Citations

Designing Complex Dynamics in Cellular Automata With Memory

Mart́ınez

Adamatzky

Alonso‐Sanz

2013

Int. J. Bifurcation Chaos

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Since their inception at Macy conferences in later 1940s complex systems remain the most controversial topic of inter-disciplinary sciences. The term 'complex system' is the most vague and liberally used scientific term. Using elementary cellular automata (ECA), and exploiting the CA classification, we demonstrate elusiveness of 'complexity' by shifting space-time dynamics of the automata from simple to complex by enriching cells with memory. This way, we can transform any ECA class to another ECA class -without changing skeleton of cell-state transition function -and vice versa by just selecting a right kind of memory. A systematic analysis display that memory helps 'discover' hidden information and behaviour on trivialuniform, periodic, and non-trivial -chaotic, complex -dynamical systems.

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Section: Wuensche's Equivalences (1992)mentioning

confidence: 99%

“…For details please see [Ninagawa, 2008]. 3,6,7,9,10,11,14,15,18,22,24,25,26,27,30,34,35,37,38,41,42,43,45,46,54,56,57,58,60,62,74,106,110,122,126,130,134,138,142,146,152,154,162,170,184.…”

Section: Wuensche's Equivalences (1992)mentioning

confidence: 99%

Section: Final Remarksmentioning

confidence: 99%

See 1 more Smart Citation

Designing Complex Dynamics in Cellular Automata With Memory

Mart́ınez

Adamatzky

Alonso‐Sanz

2013

Int. J. Bifurcation Chaos

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“…In this study we have implemented an explicit dependence in the dynamics of the past states in the manner: first summary then rule. But the order summary-rule may be inverted, i.e., the rule is first applied and a summary is then presented as new state [7,8]. This alternative memory implementation enriches the potential use of memory in discrete systems as a tool for modelling, and, again, in our opinion deserves attention on its own.…”

Section: Discussionmentioning

confidence: 97%

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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“…Research on ECAs often involves specific forms or cases of onedimensional CAs. The case of time offsets in CAs (especially ECAs) evolution has been explored, notably by Alonso-Sanz [8][9][10][11] and Letourneau [12,13]. But although related, spatial offsets have been relatively unstudied in the past.…”

Section: Introductionmentioning

confidence: 99%

Complex Behavior in Long-Distance Cellular Automata

Kang¹

2014

ComplexSystems

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The purpose of this study was to systematically explore the behavior of one-dimensional long-distance cellular automata (LDCAs). Basic characteristics of LDCAs are explored, such as universal behavior, the prevalence of complexity with varying neighborhoods, and qualitative behavior as a function of configuration. It was found that rule 73 could potentially be Turing universal through the emulation of a cyclic tag system, and that a connection between the mathematics of binary trees and Eulerian numbers might provide insight into unsolved problems.

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Elementary Cellular Automata with Memory of Delay Type

Cited by 5 publications

References 10 publications

Designing Complex Dynamics in Cellular Automata With Memory

Designing Complex Dynamics in Cellular Automata With Memory

On the Dynamics of Cellular Automata with Memory

Complex Behavior in Long-Distance Cellular Automata

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