By Gérard Y. Vichniac (auth.), E. Bienenstock, F. Fogelman Soulié, G. Weisbuch (eds.)
The NATO workshop on Disordered platforms and organic association used to be attended, in march 1985, via sixty five scientists representing a wide number of fields: arithmetic, machine technological know-how, Physics and Biology. It was once the aim of this interdisciplinary workshop to make clear the conceptual connections current among fields of analysis it seems that as diversified as: automata concept, combinatorial optimization, spin glasses and modeling of organic platforms, them all keen on the worldwide association of complicated platforms, in the community interconnected. universal to many contributions to this quantity is the underlying analogy among organic structures and spin glasses: they proportion an analogous homes of balance and variety. this is often the case for example of basic sequences of biopo Iymers I ike proteins and nucleic acids regarded as the results of mutation-selection approaches [P. W. Anderson, 1983] or of evolving organic species [G. Weisbuch, 1984]. probably the most notable features of our cognitive equipment, thinking about studying and recognttlon [J. Hopfield, 19821, is also defined when it comes to balance and variety in an appropriate configuration area. those interpretations and preoccupations merge with these of theoretical biologists like S. Kauffman [1969] (genetic networks) and of mathematicians of automata concept: the dynamics of networks of automata may be interpreted when it comes to association of a procedure in a number of attainable attractors. the current advent outlInes the relationships among the contributions provided on the workshop and in short discusses each one paper in its specific clinical context.
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E. cells in state 1 surrounded by cells in state 0 must be eliminated. Such automata may also be used in numerical simulations of physical phenomena related for instance to percolation (see the paper of Vichniac in these proceedings). Our analysis is based on a block decomposition method which leads to a macroscopic approach. e. the cells such that c(x) =I) and is denoted c = U1<=i<=p [ai' bi ], where ai <= bi and bi + 1 < ai+ 1 for any i . Hereafter, the intervals [ai' bj ] are called the components of c.
And TCHUENTE M. (1984): Iterative behaviour of one-dimensional threshold automata, Discrete Applied Mathematics, 8, pp 319-322 GOlES E. (1985): Comportement dynamique de reseaux d'automates, TMse d'etat, USMG-INPG, Grenoble. ROBERT F. (1985): Discrete Iterations, Academic Press, to appear. ROMANI F. (1976): Cellular automata synchronization, Information Sciences, 10, pp 299-318 ROSENSTIEHL P. (1966): Existence d'automates d'etats finis capables de s'accorder bien qU'arbitrairement connectes et nombreux, International Computat ion Centre Bullet in, 5, pp 215-244 TCHUENTE M.
Since there are 2k+l counting rules (out of 22k possible rules) with k inputs, the ratio of these rules (that are invariant under permutation of the inputs) drops from 1/2 to 1/16 when k varies from two to three. In this respect, when k = 2, most randomly generated rules are atypical, and emergence of order should be expected. A more elaborate reasoning, based on the ratio of forcing functions, accounts for the short periods and the spatial structure of the ordered attractors for k small[15,40,41,14].



