2- Self-Reproduction

    How far can these emergences go ? Is the apparition of life possible inside the universes of Cellular Automata ?

    The idea that it should be possible to create life inside a computer is based on the computing theory proposed by Turing. The ability of a universal Turing machine to emulate any other machine - i.e. fundamentally the fact that all sort of computers are equivalent - led von Neumann to consider how automata could self-reproduce¹⁵. He more particularly wondered "what kind of logical organization of an automaton is sufficient to produce self-reproduction"¹⁶. It is the kinematon we mentioned above.

    Some cellular automata can be used to construct universal Turing machines. The game of life is part of them. Considering the physical impossibility to realize the kinematon, we saw that von Neumann turned to the cellular automata to build his self reproductive automaton. This one was extremely complex since von Neumann considered a universal self replicator. In 1968, Edgar Codd proposed a simplified version of von Neumann's automata, that only used height states, but in this case again, Codd was considering construction universality. Things changed in the eighties with Christopher Langton. Langton considered that to study living systems inside a computer one only needs to consider necessary elements not sufficient one¹⁷. He then gave up the idea of a universal replicator.

    Langton's basic idea is that it is possible to conceive a cellular automaton supporting a structure whose components constitute the information necessary to its own reproduction. This structure is then both itself and representation of itself.

    Langton's automaton¹⁸ uses height states and twenty-nine rules. The structure that reproduces itself is a loop constituted of a sheath within which circulates the information necessary to construct a new loop i.e. necessary to reproduction.

A Langton's loop

    The cells in state 2 constitute the sheath, inner cells contain the information for reproduction. They are, in some way, the DNA of the loop. The sequences 7-0 and 4-0 propagate toward the tail. When they reach the extremity, the first ones extend the tail, the second ones construct a left-hand corner¹⁹. The addition of a "sterilization" rule that blocks the evolution after a certain number of generations leads to the construction of some kind of coral.

Langton's loops

S. Levy, Artificial Life., Penguin, 1992.

    Like von Neumann's automata, Langton's loops show that "one of the fundamental properties of living organisms, self reproduction, can be explained in terms of interactions of simple elements and that it can be studied in its logical principles independently of its physical realization"²⁰.

    Langton's loops cannot, in any way, be considered as "living", they are nothing but a limited self reproductive construction. According to Conway, if a large enough cellular space could be considered, life forms might appear within it, but it has been reckoned that it might only happen in a space of at least 10 power 10¹² cells²¹. As a reminder, the number of particles in the universe is estimated to less than 10¹⁰⁰.

    If apparition of life is envisaged, if some automata have computation universality properties, it is because these automata belong to a special category : cellular automata at the edge of chaos.

15- Adami Ch., Introduction to Artificial Life, Springer-Verlag, New-York, 1998, p. 22.

16- Shatten op. cit.

17- Adami Ch., idem, p. 27.

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

19- Langton C., Artificial Life in The philosophy of Artificial Life, Boden M. A. dir., Oxford readings in Philosophy, Oxford University Press, 1996, p. 64.

20- Heudin JC., La Vie..., op. cit., p. 54.

21- Heudin JC, L'évolution au bord du chaos, Hermès, Paris, 1998, p. 134.