CA in Urban Systems and Ecology: From Individual Behaviour to Transport Equations and Population Dynamics

Abstract

One way of seeing Cellular Automata (CA) is as cellbased computational models for describing the evolution of spatially distributed systems. Each cell represents a “local” state of the system that can vary according to its past states and to the present states of a “vicinity” of cells, following some set of relations known as “transitions rules”. More important than how these transition rules are (i.e linear, non linear, discrete, etc,), is that distant parts of such system can interact one to another only through its neighbours; in other words, what we are actually considering in CA models, is that the system obeys the principle of locality. For this seems to be the case of most systems in nature, CA models have found potential applicability in a wide variety of phenomena, ranging from macroscopic scales, like urban systems, down to microscopic scales like in solid state physics. J.F Nystrom (2001) has even argued in favour of the idea that fundamental laws of physics should arise from simple transitions rules of some Universal CA, in a structured space following R. Buckminster Fuller’s synergetic geometry. This brings us to a central point, which is that, in nature, space is as essential as time for describing any process; disregarding if we are more interested in watching at the temporal behaviour of certain group of state variables or if we are more interested in taking static pictures of some distributed properties in space, there will be always a spatiotemporal evolution process taking place behind. A good example are urban and environmental systems; social scientists have been discussing since long ago how population and economy of regions interact and evolve through the years, while geographers and urban analysts have been doing it looking at its spatial structures. Both have contributed in equal parts to our present understanding of sustainable development. However, ?can economists explain development without considering where was located the infrastructure support? or ?can urbanists explain the structure of a city without considering the historical circumstances? Both views tend to describe one aspect of the evolution looking at the other as frame constrains, usually given in terms of literal stories. The same happens in many other fields of science treating with complexity. A more modern view stands on the growing availability of informatics tools, and pushes towards constructing spatiotemporal models. But this is not a simple task; most attempts