Managing Spatial Self-organization via Collective Behaviors

Spatial self-organizations appear in many natural and artificial systems. Spatial systems creation and development, called morphogenesis, is the subject of many research studies since many years (1). Fractal computation approach is, for exemple, one of the methods proposed to deal with such studies. But, even if this method is able to describe unlimited local formations on multi-scale descriptions, the formation process itself is described in a global way. The goal of this paper is to introduce the distributed and decentralized computing as a general methodology to propose emergent spatial formation, able to deal with local perturbations and with non homegeneous formation rules. We propose a study case on Schelling Model dealing with interacting population over an environment based on a regular grid. SPATIAL MORPHOLOGY MODELLING ON THE EDGE OF COMPLEXITY The study of spatial morphology is a major aspect of the understanding of many phenomena for natural or artificial systems. Living systems or social systems, for example, are systems where the spatial formation has a high meaning and modifies deeply by itself the system evolution. The system evolution leads to modify itself the spatial formations by feed-back processes. Spatial morphology models can be classified by many criteria. Some of these models are static (finding the optimal shape of some problem) or dynamic (morphogenesis, for example). When the models involve dynamical processes, these dynamics can be expressed in a global way, like we do using partial differential equations: the objective of the system description consists in describing the different phenomena involved (diffusion, transport, ...). Spatial morphology systems can be involved inside a multi-scale processus, giving some specific properties to this multi-scale formation, like the development of important exchange area. Fractal systems are well-known to model these multi-scale systems like fractal shape of plants. Even if these fractal geometries are able to model multi-scale descriptions, they are generally completly deterministic and they are not suitable to describe geometrical evolutions or to integrate local disturbations. For this purpose, we need to change the model concept and go from global deterministic models to decentralized approaches where the whole system is only known (or emerge) by the interaction system of behavior population. SCHELLING MODEL EXTENSION IN ORDER TO MODEL SELF-ORGANIZATION BY MEANING OF MULTI-CRITERIA SYSTEM SEPARATION Thomas Schelling’s city segregation model illustrates how spatial organizations can emerge from local rules, concerning the spatial distribution of people which belong to different classes. In this model, people can move, depending on their own satisfaction to have neighbours of their own class. Based on this model, a city can be highly segregated even if people have only a mild preference for living among people similar to them. In this model, each person is an agent placed on a 2D grid (in his original presentation, a chessboard was used by Thomas Schelling). Each case can be considered like a house where the agent lives. Each agent cares about the class of his immediate neighbours who are the occupants of the abutting squares of the chessboard. Each agent has a maximum of eight possible neighbours. He computes the rate of the neighbours of its own class ha l-0 04 30 56 5, v er si on 1 9 N ov 2 00 9 Author manuscript, published in "ESM'2008, Le Havre : France (2008)"