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Scientific modeling with cellular automata

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Cellular automata provide a simple environment in which to discretize time and space in order to investigate natural phenomena. In a two‐dimensional scenario for example, the action usually takes place in a rectangular array of cells (although other cell shapes can be used) and each cell exists in one of several ‘states’. In discrete time‐steps all cells change their state in unison according to a locally prescribed rule that takes into account the state of each cell's neighbors at the previous time‐step. This elementary but powerful framework has been highly successful in modeling various scientific phenomena from a broad spectrum of disciplines, some of which are reviewed in this article. Both qualitative and quantitative data can be obtain by the cellular automata approach. This article is categorized under: Algorithms and Computational Methods > Computational Complexity Applications of Computational Statistics > Computational and Molecular Biology Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods
A cellular automaton random array with some cells alive (black) and the rest dead (white). Often the grid lines are suppressed as they are considered superfluous.
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Neritina ziczac (left) and the CA model by Kusch and Markus of its pigmentation pattern.
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The unremarkable looking Rule 110 that has the extraordinary power of a desktop computer.
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The evolution (downward) of Rule 150 from a single black cell and all the others white. Some organization is clearly taking place here.
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Rule 150 illustrating the subsequent state of the central cell from the eight possible configurations of three adjacent cells in two colors. Note that the output in binary, 10010110, is the number 150 and this is the manner in which all the 256 elementary one‐dimensional, two‐state rules are numbered.
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Snow crystal forms obtained by the CA model of Reiter.
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Some of the snow crystals that evolve from the Packard elementary CA model starting with a single black seed on a hexagonal array.
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The CA model of steady‐state heat flow into a rectangular region that satisfies the boundary condition of 100° along the top side and 0° on each of the other three sides.
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The typical wave like structure found with a Greenberg‐Hastings model.
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The playing out of the Game of Life from a random initial configuration after the elapse of more than 1300 time steps. The sideways ‘V’ shaped figure at the center of the array is known as a ‘glider’—it moves in an ungainly diagonal motion across the screen. It will shortly be annihilated by the three live horizontal cells just above it. In this implementation the normally white cells are gray and the grid lines white.
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The equilibrium state of the VOTE cellular automaton with 60% of the initial configuration of cells in the white (0) state.
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Here we have depicted the commonly used Moore neighborhood (left) of a central cell consisting of its eight immediate neighbors. Another neighborhood that can be considered is the von Neumann neighborhood consisting of the cells immediately to the N, S, E, W of a particular cell.
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Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods
Applications of Computational Statistics > Computational and Molecular Biology
Algorithms and Computational Methods > Computational Complexity

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