On transition rules of complex structures in one-dimensional cellular automata: Some implicaltions for urban change

We propose a new algorithm to build self-organizing and self-repairing marine structures on the ocean floor, where humans and remotely operated robots cannot operate. The proposed algorithm is based on the one-dimensional cellular automata model and uses simple transition rules to produce various complex patterns. This cellular automata model can produce various complex patterns like sea shells with simple transition rules. The model can simulate the marine structure construction process with distributed cooperation control instead of central control. Like living organism is constructed with module called cell, we assume that the self-organized structure consists of unified modules (structural units). The units pile up at the bottom of the sea and a structure with the appropriate shape eventually emerges. Using the attribute of emerging patterns in the one-dimensional cellular automata model, we construct specific structures based on the local interaction of transition rules without using complex algorithms. Furthermore, the model requires smaller communication data among the units because it only relies on communication between adjacent structural units. With the proposed algorithm, in the future, it will be possible to use self-assembling structural modules without complex built-in computers.

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COMPLEX DYNAMICS OF ELEMENTARY CELLULAR AUTOMATA EMERGING FROM CHAOTIC RULES

International Journal of Bifurcation and Chaos ◽

10.1142/s021812741250023x ◽

2012 ◽

Vol 22 (02) ◽

pp. 1250023 ◽

Cited By ~ 20

Author(s):

GENARO J. MARTÍNEZ ◽

ANDREW ADAMATZKY ◽

RAMON ALONSO-SANZ

Keyword(s):

Cellular Automata ◽

Complex Dynamics ◽

Chaotic Behavior ◽

Mean Field Theory ◽

Mean Field ◽

One Dimensional ◽

Time Dynamics ◽

Transition Rules ◽

State Transition Rules ◽

With Memory

We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behavior. CA are well-known computational substrates for studying emergent collective behavior, complexity, randomness and interaction between order and chaotic systems. A number of attempts have been made to classify CA functions on their space-time dynamics and to predict the behavior of any given function. Examples include mechanical computation, λ and Z-parameters, mean field theory, differential equations and number conserving features. We aim to classify CA based on their behavior when they act in a historical mode, i.e. as CA with memory. We demonstrate that cell-state transition rules enriched with memory quickly transform a chaotic system converging to a complex global behavior from almost any initial condition. Thus, just in few steps we can select chaotic rules without exhaustive computational experiments or recurring to additional parameters. We provide an analysis of well-known chaotic functions in one-dimensional CA, and decompose dynamics of the automata using majority memory exploring glider dynamics and reactions.

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Efficient Solutions of the Density Classification Task in One-Dimensional Cellular Automata: Where Can They Be Found?

Complex Systems ◽

10.25088/complexsystems.29.3.669 ◽

2020 ◽

Vol 29 (3) ◽

pp. 669-688

Author(s):

Zakaria Laboudi ◽

Keyword(s):

Cellular Automata ◽

Efficient Solutions ◽

Classification Task ◽

One Dimensional

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On Uniqueness of the Wulff Shape for Cellular Automata

Fundamenta Informaticae ◽

10.3233/fi-1991-14104 ◽

1991 ◽

Vol 14 (1) ◽

pp. 75-89

Author(s):

Paweł Wlaź

Keyword(s):

Cellular Automata ◽

Large Class ◽

Growth Function ◽

Wulff Shape ◽

Transition Rules

In this paper, ordered transition rules are investigated. Such rules describe an increment of mono-crystals and for every rule one can calculate so called Wulff Shape. It is shown that for some large class of these rules, there exists at most one growth function which generates a given Wulff Shape.

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