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Fractal geometry is being used to model cities using ideas from cellular automata.

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Presentation on theme: "Fractal geometry is being used to model cities using ideas from cellular automata."— Presentation transcript:


2 Fractal geometry is being used to model cities using ideas from cellular automata


4 Fractal Britain

5 Scale and fractals: physics gets in on the act

6 Simple CA simulating fractal patterns

7 Many Seeds – like DLA crystal growth




11 t h i r d w o r l d c i t i e s: chaotic and discontinuous spatial patterns rapid and unorganised development process. Due to these very same characteristics, these cities are seen as excellent objects for the study of complex systems. Urban growth in the Latin American context is characterised by the formation of peripheral spontaneous settlements, which are, in most cases, low-income residential areas. This process, called ´peripherisation´, is understood as the normal process of growth of Latin American cities On the periphery consists in a morphological analysis and simulation of urban growth, focusing on a specific urban context: Latin American cities.

12 Two aspects of this process are currently being studied in 2 projects: p e r i p h e r i s a t i o n p r o j e c t Social Pyramid Peripherisation project is based on the development of a series of heuristic simulation models using agent-based techniques. The model aims to demonstrate and explore the dynamics of urban growth through the production and transformation of peripheral spontaneous settlements. The project is based on the relation between the economic constitution of the Latin American society (social pyramid) and the emergent spatial pattern of these cities. t = 300t = 800t = 1200 Some of the traditional issues of Latin American rapid urban development are analysed in the light of complexity theory. Preliminary results suggest that some assumptions as the relation between speed and spatial pattern, for instance, may be questioned.

13 c i t y - o f - s l u m s p r o j e c t Self-organisation across scales It is a joint project with Fabiano Sobreira which aims to discuss the role of self- organisation in the spatial dynamics of Third World cities, by exploring self-organisation in two different scales: settlement formation and urban growth. City-of-slums is an agent-based model that focuses on the process of consolidation of inner-city squatter settlements within a peripherisation process. the resulting urban morphology, although related to distinct scales, present similar degree of fragmentation (fractal pattern); these two complex processes are involved in a spatial logic in which resistance is the cause, consolidation is the process and fragmentation is the result. Preliminary results: t = 100t = 300t =800t = 1000

14 Cooperating with the Brazilian Centre for Space Research (INPE) which developed an object oriented GIS (SPRING) and an open source GIS library called TerraLib, further application is going to be the use of these models for urban growth simulation of Brazilian cities including parts of Sao Paulo city. Sao Paulo city region, a complex urban environment with a population larger then 18 million people


16 Crowd density Public safety – an ambulance trying to cross the parade



19 The parade A swarm of agents searching the space but without any constraints on space

20 The swarms without any street geometry

21 With street geometry

22 6. Designing and Testing New Routes There are six routes which were given to Intelligent Space by the GLA and Westminster – essentially we are engaged in what if analysis, not in suggesting new routes The general principles are to break the loop of the carnival and reduce densities. The six schemes are

23 Alternative Routes

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