0209

AUTOMATON (Cellular) 2)

1.An abstract device able to transform itself.

The concept of a cellular automaton has been developped by A. TURING (1950) and John von NEUMANN (1956) and also somehow by W. Mc CULLOCH and W. PITTS (Their formal neuron model)

F. HEYLIGHEN describes cellular automata as "� mathematical models of distributed dynamical processes characterized by a discrete space and time" (F. HEYLIGHEN, 1997, p.33)

The conditions for the construction of a cellular automaton are as follows:

- an unlimited and uniform substrate, which constitutes a perfectly isotropic environment

- identical elements or cells, with defined properties

- an initial configuration, conSisting of number of cells

- definite rules of transformation

The basic characteristic of cellular automata is the emergence of complex organization obtained from simple rules.

Numerous varieties of cellular automata have been proposed. The best known are those in CONWAY's Game of Life. However MARUYAMA has used one as early as 1963 as an example of "deviation-amplifiying mutual causal processes".

As to the rules of transformation, some are not deductible from any previous configuration ("Garden of Eden")

In some cases the rules of transformation are themselves embedded within the initial configuration.

2. A network composed of elements (nodes), each of whom is an elemental device able to perform some elemental calculation.

Every element of the cellular automaton may be considered itself an automaton if its operation rules are included. According to A.G. BARTO: "Cellular automata are networks of identical automata which are interconnected in a regular way with the automata having neighboring positions in the network" (1978, p.165)

B.R. GAINES and L.J. KOHOUT state: "�an automaton is a discrete-time, discrete-state-space, state determined machine" (1976, p.192)

Each element processes a limited number of possible binary states.

The automaton evolves step by step, in a discontinuous way, according to the rules impose to its elements, which determine at each step the state of each node according to its preceeding state and the states of the neighbouring nodes.

Curiously, a very complex global behavior may emerge from the application of quite simple rules at local level.

GAINES and KOHOUT state: "� neither the actual current state of an automaton nor its current input are necessarily well-defined. For example, we may know only the probability distribution of possible current states, or of possible current inputs. In either case the next state of the automaton will not be necessarily a single state but will probably also be known only as a distribution" (Ibid)

ASHBY has given interesting examples of such ergodic systems, whose repertory of all possible states is resumed in a markovian matrix. (1956)

According to GAINES and KOHOUT: "It is a convenient generalization of the concept of an automaton to consider transitions not just between states but between such states distributions, regarding distributions over states and inputs as generalized "states" and "inputs" respectively" (Ibid).

These authors propose the corresponding terminology of hyperstates and hyperinputs.

The automaton model is nowadays basic to the study of so-called neural networks, connection machines and distributed artificial intelligence.

It may even become very useful for the description of social systems in general.

2) methodology or model

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