Análise fractal de formas urbanas: estudo sobre a dimensão fractal e o Índice de Desenvolvimento Humano Municipal (IDHM)

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Costa, Paulo Cesar da
Stump, Sandra Maria Dotto
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Silva, Leandro Nunes de Castro
Pereira, Sérgio Luiz
Engenharia Elétrica
The concepts of fractal geometry, which were developed in 1975 by Mandelbrot, complement Euclidean geometry as they provide theoretical dimensional fundamentals for shapes whose irregularities cannot be properly interpreted by classical topological definitions. The standards of this irregular morphology, found in abundance in nature, can be recognized in the construction processes of various fractals anthropic figures, mainly when combined with computational technology. Professionals and researchers from several knowledge fields are exploring these concepts to simulate or create models of irregular shapes, with detail levels hitherto inconceivable. Earth sciences supported by geotechnologies have great potential for applying Mandelbrot s theories as a conceptual reference for analyzing phenomena presenting fractal behaviors, belonging to different application areas as geomorphology, climatology and urban and landscapes studies. In this approach, the fractal dimension of the territorial space occupied by cities is considered an indicator for understanding occupation patterns as one of the factors to be considered in urban planning policies, e.g., to propose projects for more appropriate investments distribution and development of infrastructure. In this work, these concepts were applied by using the box-counting method to calculate the fractal dimension of urban forms from eight Brazilian state capitals by using the Municipal Human Development Index (MHDI) as the selection criteria: four cities ranked among the top of the list and four cities classified among the last positions of the state capitals. The results were analyzed in order to identify possible relationships or trends among these indicators, namely, fractal dimension and MHDI, that may support future studies and urban planning. These relationships were not confirmed: the eight studied cities presented heterogeneous fractal dimension values and no trends were verified. However, it was concluded that the fractal dimension of urban form is related to its scattering pattern and occupation over the geographical territorial space and may be an indicator of the occupation density from the urban area.
geometria fractal , estudos urbanos , dimensão fractal , políticas de planejamento urbano , método da contagem de quadrados , formas urbanas , Índice de Desenvolvimento Humano Municipal , fractal geometry , urban studies , fractal dimension , urban planning policies , boxcounting method , urban forms , Municipal Human Development Index
COSTA, Paulo Cesar da. Análise fractal de formas urbanas: estudo sobre a dimensão fractal e o Índice de Desenvolvimento Humano Municipal (IDHM). 2014. 89 f. Dissertação (Mestrado em Engenharia Elétrica) - Universidade Presbiteriana Mackenzie, São Paulo, 2014.