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agent-based models agents aggregate applications associated attraction available land average Batty begin behavior cellular automata central chapter clusters complex computed constraints defined density destinations diffusion diffusion-limited aggregation distance distribution dynamics edge cities effect emerge equation example exist explore focus fractal dimension function geometry global gradient grid grow growth process growth rate ideas illustrate implies increases initial interac interaction introduced involves kind landscape logistic growth measure ment Moore neighborhood morphology move movement nodes noise origins parade parameter values paths patterns percent period phase transition physical pixels population positive feedback potential power law problem random randomly rank-size relations redevelopment returns to scale routes scale seed segregation self-organized criticality self-similarity shown in figure simulation spatial structure street symmetric takes place theory threshold tion tracks transition rules types urban development urban growth urban systems various walk waves