ABSTRACT
In this chapter, we introduce a technique of simulation that articulates the system of interest as a set of cells, in our case, a 2D tessellation of cells that pertain to different land uses or socioeconomic activities that define cities. Cellular automata (CA) are defined in such a way that these cells change state, from one land use to another, for example, dependent on a series of rules that define the way these land uses influence one another, usually in very local neighbourhoods around each cell in question. This is the way local action translates into global patterns, and CA tend to be the essential mechanism that determines how global patterns emerge from local order which can often be interpreted as geometries and spatial morphologies that are fractals. Having introduced CA, we then outline the idea of fractals which have structures across many spatial and/or temporal scales that are similar to one another at each scale. The classic example is a tree-like structure or any hierarchical object such as the set of nested road systems from freeways to local streets or the set of markets and retail centres which define the hierarchy of central places. CA, of course, can be used to represent other local processes such as forest fires and a variety of percolation phenomena that translate into ordered patterns at higher levels and are not restricted to cities. Having introduced CA, we then develop a generic equation for spatial processes based on reaction-diffusion and introduce ideas about fractals. We consider different
Abstract ............................................................................................................................................23 2.1 Cellular Automata, GeoComputation and Fractal Morphologies ..........................................24 2.2 Elements of Strict CA .............................................................................................................25 2.3 Origins of CA .........................................................................................................................28 2.4 Neighbourhoods, Transitions and Conditions ........................................................................29 2.5 The Generic Model: Reaction and Diffusion ......................................................................... 31 2.6 Origins of Fractal Geometry and Morphology.......................................................................34 2.7 Simulating Fractal Growth Using CA .................................................................................... 35 2.8 More Complicated Growth Regimes ...................................................................................... 39 2.9 Applications to Cities and Related Ecologies ......................................................................... 41 2.10 Conclusions .............................................................................................................................44 2.11 Further Reading ......................................................................................................................44 References ........................................................................................................................................ 45
kinds of patterns that are generated by CA giving various examples in the 2D domain, and we then illustrate how these kinds of models have been used to simulate urban development patterns. We develop a number of critiques of this modelling approach, review the key historical and contemporary literature and then present relevant references.
