Abstract
In Twenty Problems in the Theory of Cellular Automata, Stephen Wolfram asks “how common computational universality and undecidability [are] in cellular automata.” This papers provides elements of answer, as it describes how another universal cellular automaton than the Game of Life (Life) was sought and found using evolutionary algorithms. This paper includes a demonstration that consists in showing that the presented R automaton can both implement any logic circuit (logic universality) and a simulation of Life (universality in the Turing sense).
All the elements of the evolutionary algorithms that were used to find R are provided for replicability, as well as the analytical description in R of a cell of Life.
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References
Wolfram, S.: Universality and complexity in cellular automata. Physica D 10, 1–35 (1984)
Gardner, M.: The fantastic combinaisons of john conway’s new solitaire game “life”. Scientific American (1970)
Gardner, M.: On cellular automata, self-reproduction, the garden of eden, and the game of life. Scientific American 224, 112–118 (1971)
Dytham, C., Shorrocks, B.: Selection, patches and genetic variation: A cellular automata modeling drosophila populations. Evolutionary Ecology 6, 342–351 (1992)
Epstein, I.R.: Spiral waves in chemistry and biology. Science, 252 (1991)
Ermentrout, Lotti, G., Margara, L.: Cellular automata approaches to biological modeling. Journal of Theoretical Biology 60, 97–133 (1993)
Wolfram, S., Packard, N.H.: Two-dimensional cellular automata. Journal of Statistical Physics 38, 901–946 (1985)
Berlekamp, E., Conway, J.H., Guy, R.: Winning ways for your mathematical plays. Academic Press, London (1982)
Rendell, P.: Turing universaility of the game of life. In: Adamatzky, A. (ed.) Collision-Based Computing, Springer, Heidelberg (2002)
Wolfram, S.: Twenty problems in the theory of cellular automata. Physica Scripta, 170–183 (1985)
Margolus, N.: Physics-like models of computation. Physica D 10, 81–95 (1984)
Lindgren, K., Nordahl, M.: Universal computation in simple one dimensional cellular automata. Complex Systems 4, 299–318 (1990)
Morita, K., Tojima, Y., Katsunobo, I., Ogiro, T.: Universal computing in reversible and number-conserving two-dimensional cellular spaces. In: Adamatzky, A. (ed.) Collision-Based Computing, Springer, Heidelberg (2002)
Adamatzky, A.: Universal dymical computation in multi-dimensional excitable lattices. International Journal of Theoretical Physics 37, 3069–3108 (1998)
Banks, E.R.: Information and transmission in cellular automata. PhD thesis, MIT (1971)
Bays, C.: Candidates for the game of life in three dimensions. Complex Systems 1, 373–400 (1987)
Sapin, E., Bailleux, O., Chabrier, J.J.: Research of complex forms in the cellular automata by evolutionary algorithms. In: Liardet, P., Collet, P., Fonlupt, C., Lutton, E., Schoenauer, M. (eds.) EA 2003. LNCS, vol. 2936, pp. 373–400. Springer, Heidelberg (2004)
Sapin, E., Bailleux, O., Chabrier, J.J.: Research of a cellular automaton simulating logic gates by evolutionary algorithms. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 414–423. Springer, Heidelberg (2003)
Dewdney, A.: The planiverse. Poseidon Press (1984)
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Sapin, E., Bailleux, O., Chabrier, JJ., Collet, P. (2004). A New Universal Cellular Automaton Discovered by Evolutionary Algorithms. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24854-5_16
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DOI: https://doi.org/10.1007/978-3-540-24854-5_16
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