International Encyclopedia of Systems and Cybernetics

This model was introduced by M. MARUYAMA in 1963. He observed that the classical model of cybernetics was "focusing on the deviation-counteracting aspect of the mutual causal relationship, (but that) cyberneticians paid less attention to the systems in which the mutual causal effects are deviation-amplifying". He noted that the latter: "… are ubiquitous: accumulation of capitals in industry, evolution of living organisms, the rise of cultures of various types, interpersonal processes which produce mental illness, international conflicts, and the processes that are loosely termed as "vicious circles" and "composed interests"; in short, all processes of mutual causal relationships that amplify an insignificant or accidental initial kick, build up deviation and diverge from the initial condition" (p.233).

He called the study of these processes "the second cybernetics" (not to be confused with von FOERSTER's cybernetics of 2d order). He observed that: "The deviation-counteracting mutual causal process is also called "morphostasis", while the deviation-amplifying one is called "morphogenesis" (Ibid).

The similarities with various processes and models discovered later on is evident: dissipative structuration, bifurcations, sensibility to initial conditions, and chaos.

He stated, for example: "… when the deviation amplification mutual causal process is combined with indeterminism, here again a revision of a basic law becomes necessary. The revision states: A small initial deviation, which is within the range of high probability, may develop into a deviation of very low probability (or more precisely, into a deviation which is very improbable within the framework of probabilistic unidirectional causality). Not only the law of causality, but also the second law of thermodynamics is affected by the deviation amplifying mutual causal process" (p.234).

MARUYAMA proposed the following simple model of the deviation amplifying mutual causal process (practically a cellular automata, complete with graphic representation):

"Let us imagine, for the sake of simplicity, a two-dimensional organism. Let us further imagine that its cells are squares of an equal size. Let us say that the organism consists of four types of cells: green, red, yellow and blue. Each type of cell reproduces cells of the same type to build a tissue. A tissue has at least two cells. The tissue grows in a two-dimensional array of squares. Let us give a set of rules for the growth of tissues:

"1. No cells die. Once reproduced, a cell is always there.

"2. Both ends of a tissue grow whenever possible, by reproducing one cell per unit time in a vacant contiguous square. If there is no vacant contiguous square at either end, that end stops growing. If there are more than one vacant contiguous squares at either end, the direction of the growth is governed by the preferential order given by rules 3,4, and 5.

"3. If, along the straight line defined by the end cell and the penultimate cell (next to the end cell) there are less than or equal to three cells of the same type (but may be of different tissues) consecutively, the preferred direction is along the same straight line. If that direction is blocked, follow rule 5.

"4, If, along the straight line defined by the end cell and the penultimate cell, there are more than or equal to four cells of the same type (but may be of different tissues) consecutively, the preferred direction of growth is a left turn. If a left turn is impossible, make a right turn.

"5. If, when a straight growth is preferred, the straight growth is impossible because the next square is already occupied, do the following. If the square to which the straight growth would take place is filled with a cell of the same type as the growing type, make a left turn. It the square ahead is filled with a cell whose type is different from that of the growing tissues, make a right turn.

"6. The growth of the four types of tissues is timewise out of phase to each other: green first, red second, yellow third, and blue last within a cycle of one unit of time" (p.237).

MARUYAMA's rules are practically framing algorithms.

A very important feature of the model is the initial state, i.e. the disposition of the first four units on the grid (MARUYAMA's "initial kick"). And, of course, the player is furnishing the energy for the process of construction.

(This kind of graphical experience is much less complicated in practice that would appear by reading the rules).

MARUYAMA's graphics are self-structuring, i.e. self-constraining, in accordance with the chosen rules, which may be widely varied. This is very significant for concrete systems, which are always based on ruled interrelations between some more or less reduced types of elements. CONWAY's games of life are of the same kind, even if based on quite different rules.

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