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Introduction to Cellular Automata
History
The Game of Life
Other Cellular Automata
Applications
Cellular Automata and Artificial Life
Emergence
Self-Reproduction
Chaos and complexity
Bibliography



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    Conclusion

    Cellular automata are abstract structures which make it possible to study virtual completely known universes. They help us to understand our Universe : "Thus complex physical and biological systems may lie in the same universality classes as the idealized mathematical models provided by cellular automata. Knowledge of cellular automaton behaviour may then yield rather general results on the behaviour of complex natural systems."31.

    The universal computation capability of some cellular automata, i.e. their capability to construct arbitrary complex structures, is not sufficient to prove the possibility of life apparition in these universes. Generalization of cellular automata behaviours to our Universe is not direct and its pertinence is hard to be proved. However, and as a conclusion, I let you think about the two following images.

Norman Packard's snowflake
Norman Packard's snowflake
S. Levy, Artificial Life, Penguin, 1992.

 

A real shell texture and its equivalent generated with a cellular automaton
Shells
Langton ed., Artificial Life an overview, MIT press, 1997.


31- Wolfram S., Idem.


    Bibliography

Adami Ch., Introduction to Artificial Life, Springer-Verlag, New-York, 1998.

Bertalanffy (von) L., Théorie générale des systèmes. Dunod, Paris, 1973.

Gutowitz H.A., Langton C.G., Methods for designing Cellular Automata with "Interesting" Behavior, 1994. Available at : http://www.santafe.edu/~hag/interesting/interesting.html.

Heudin JC, La Vie Artificielle, Hermès, Paris, 1994.

Heudin JC, L'évolution au bord du chaos, Hermès, Paris, 1998.

Langlois A., Phipps M., Automates cellulaires. Application à la simulation urbaine. Hermès, Paris, 1997.

Langton C.G., Studying Artificial Life with cellular automata, Physica D 22, 1986.

Langton C.G., Life at the edge of chaos, Artificial Life II, Addison-Wesley, 1991.

Langton C.G., Artificial Life in The philosophy of Artificial Life, Boden M. A. dir., Oxford readings in Philosophy, Oxford University Press, 1996.

Langton ed., Artificial Life. An overview, MIT press, 1997.

Levy S., Artificial Life. The quest for a new creation, Penguin, 1992.

Michell M., Hraber P.T., Crutchfield J., Revisiting the edge of chaos : Evolving Cellular Automata to perform Computations, Santa Fe Institute, Working Paper 93-03-014. Available at : http://www.santafe.edu/projects/evca/Papers/rev-edge.html

Morin E., La Méthode. I-La Nature de la Nature., Points, Seuil, Paris 1977.

Rosnay (de) J., Le macroscope. Vers une vision globale. Points, Seuil, Paris, 1975.

Rucker R., Walker J., Introduction to CelLab, http://www.fourmilab.ch/cellab/

Shatten A., Cellular Automata, Institute of General Chemistry Vienna University of Technology, Austria, 1997.

Toffoli T., Cellular automata as an alternative to Differential equations, in Modelling Physics, Physica 10D, 1984.

Von Neumann J. et Burks A. ed., Theory of Self-Reproduction Automata, University of Illinois Press, 1966.

Wolfram S., Universality and complexity in cellular automata, Physica D, 10:1-35, 1984. Available at : http://www.stephenwolfram.com/publications/articles/ca/84-universality/index.html


Jean-Philippe Rennard Ph.D. 12/2000.
http://www.rennard.org/alife
alife@rennard.org

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