International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.


The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.


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.


  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
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Bertalanffy Center for the Study of Systems Science(2020).

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