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Network View of Conway's Game of Life

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Conway's Game of Life, or simply Life, is one of the most famous cellular automata. The main purpose of this Demonstration is to present a network representation of Life that focuses on the effective relationships between cells rather than their states [1]. The Life network is derived from a one-cell perturbation of all cells. The effect of the perturbation of each cell propagates to other cells after a time interval. We regard the influence of this propagation as effective relationships between cells and connect them by directed links that are drawn with a gradient in color from red to green. The networks derived from typical patterns have a distinctive feature arising from the dynamical aspect of each pattern [2].

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The typical Life patterns can be chosen in the dropdown menu. You click a cell to change its state.

The numbers in parentheses after the preset configuration choices are the number of steps needed for a repetition of that original configuration.

The "update one step" button draws links when the "draw links" check box is checked. This check means that a one-cell perturbation is added to all cells. The "interval" means an interval of time steps between the time when the "draw links" is checked and the present time (total time steps). The restricton that the maximum interval is is set to avoid repetitions that come from the periodic boundary conditions, where is the edge size and [ ] is the greatest integer function.

The control "density" is used for the "Random" setting of the preset configurations.

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Contributed by: Yoshihiko Kayama (May 2012)
Open content licensed under CC BY-NC-SA

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References

[1] Y. Kayama, "Network Representation of Cellular Automata," in 2011 IEEE Symposium on Artificial Life (IEEE ALIFE 2011) at SSCI 2011, 2011 pp. 194–202.

[2] Y. Kayama, and Y. Imamura, "Network Representation of the Game of Life," Journal of Artificial Intelligence and Soft Computing Research, 1(3) pp. 233–240.

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