
Artificial life 

Introduction
to Cellular Automata  
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 selfreproduce^{15}.
He more particularly wondered "what kind of logical
organization of an automaton is sufficient to produce
selfreproduction"^{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 one^{17}. 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 automaton^{18} uses height states and twentynine 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 70 and 40 propagate toward the tail. When they reach the extremity, the first ones extend the tail, the second ones construct a lefthand corner^{19}. 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 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 10^{12} cells^{21}.
As a reminder, the number of particles in the universe is
estimated to less than 10^{100}. 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, SpringerVerlag, NewYork, 1998, p. 22. 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. 
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