Self-organization and Chaos in Collective PhenomenaThe Combinatory Systems view

If we accept the traditional definition of self-organization as a macro behaviour in which the micro behaviours appear to be directed, or organized, by an invisible hand in order to produce the emerging phenomenon represented by the formation of ordered structures, of recognizable patterns, then all five of the collective phenomena can be defined as self-organization. To understand, explain and, to a certain extent, control these collective phenomena I suggest the simple Theory of Combinatory Systems. By Combinatory System I mean an unorganized system made up of a plurality of similar elements; the macro behaviour of the system, as a unit, derives from the combination of the analogous behaviours of its similar elements, according to a feedback relation between micro and macro behaviours. This internal feedback between micro and macro behaviours guarantees the maintenance over time of the system’s macro behaviour and directs the micro behaviour When the system starts up “by chance”, it then maintains its behaviour “by necessity”, as if a Supreme Authority regulated its time path and produced the observable effects and patterns. This paper presents the fundamental ideas and mechanisms that underlie these systems and some models showing the action of the self-organization. Because of the extreme wealth of literature on systems I’ve made the choice to mention only the fundamental and well known (or the very specific) contributions and web sites.