Cellular Automata and Fractal Urban Form: A Cellular Modelling Approach to the Evolution of Urban Land-Use Patterns

Abstract

Cellular automata belong to a family of discrete, connectionist techniques being used to investigate fundamental principles of dynamics, evolution, and self-organization. In this paper, a cellular automaton is developed to model the spatial structure of urban land use over time. For realistic parameter values, the model produces fractal or bifractal land-use structures for the urbanized area and for each individual land-use type. Data for a set of US cities show that they have very similar fractal dimensions. The cellular approach makes it possible to achieve a high level of spatial detail and realism and to link the results directly to general theories of structural evolution.

A highly detailed land-use vector map for Madrid region based on photo-interpretation

“…MLU can also be used as a basis for dynamic models of urban LULC change such as cellular automata models (Barredo, Demicheli, Lavalle, Kasanko, & McCormick, 2004;Batty, Xie, & Sun, 1999;White & Engelen, 1993), or agent-based models (Brown, Page, Riolo, Zellner, & Rand, 2005;Veldkamp & Verburg, 2004). Future work is likely to include the incorporation of LULC information for new neighboring regions that are usually considered to fall under the influence of the Madrid metropolitan region, such as Toledo, Segovia and Guadalajara.…”

Ecological benefits assessment and spatial modeling of urban ecosystem for controlling urban sprawl in Eastern Beijing, China

“…CA was first proposed by Ulam in the 1940s and soon used by Von Neumann to investigate the logical nature of self-reproducible systems (White and Engelen, 1993). Thereafter, CA was prevalently used to simulate complex geographical phenomena , especially for urban simulation.…”

“…The application of CA in urban expansion modeling can give insights into a wide variety of urban phenomena (Li and Yeh, 2002). Urban CA models have better performance in simulating urban growth and expansion than conventional urban models because they are much simpler than complex mathematical equations, but produce results that are more meaningful and useful with intuitive results (Deadman et al, 1993;White and Engelen, 1993;Wu, 1998). Its applications differ from the typical natural systems applications in that they tend to have a very limited total number of cells and a small number of temporal iterations (Batty and Xie, 1994).…”

“…A variety of approaches have been used to model the spatial process of urban expansion, such as Markov chains (Ló pez et al, 2001) and spatial logistic regression (Cheng and Masser, 2003). In recent years, Cellular Automata (CA) techniques have gained attention as modeling tools for urban expansion process simulation (AlAhmadi et al, 2009;Barredo et al, 2003;Batty and Xie, 1994;He et al, 2008;He et al, 2006;Li and Yeh, 2000;Liu et al, 2008;Stevens et al, 2007;White and Engelen, 1993;Wu, 1998). The application of CA in urban expansion modeling can give insights into a wide variety of urban phenomena (Li and Yeh, 2002).…”

Space For The Unccd And The Desertwatch Project

“…For each simulation step (in these simulations the time step is set to 1 year) the system will try to meet the overall demand for each land use class, starting to change the pixels with highest transition potential, until the total demand is met. The core algorithm, based on the cellular automata paradigm, is described in detail in [16], [17], [18], [19] and [20]. The major input variables are listed hereafter:…”