Abstract
Cities are complex systems and their physical forms are the manifestation of cultural, social and economic processes shaped by the geometry of natural and man-made elements. Digital Surface Models (DSM) using LiDAR provide an efficient volumetric transformation of urban fabric including all built and natural elements which allows the study of urban complexity through the lens of fractal dimension (D). Founded on the “box-counting” method, we reveal a voxelization technique developed in GIS (Geographic Information System) to estimate D values of ten DSM samples across central Melbourne. Estimated D values of surface models (between 2 and 3) provide a measure to interpret the structural complexity of different urban characters defined by the pattern of developments and densities. The correlations between D values with other DSM properties such as elevation, volume, solar radiation and surface roughness, showed a strong relationship between DSM volume and mean elevation. Lower strength correlations were recorded with solar radiation and surface roughness. The proposed method provides opportunities for fractal research to study pressing issues in complex urban environments such as declining physical fitness, mental health and urban biodiversity.
Highlights
Urban environments are complex systems whose physical forms are the manifestation of cultural, social and economic processes shaped by the geometry of the natural and man-made world [1]
The das has been captured in Map Grid of Australia (MGA) Zone 55 projection and saved in the XYZ coordinated in 1 km × 1 km
The voxelization method resulted in a set of D values that could be used to compare other sample attributes
Summary
Urban environments are complex systems whose physical forms are the manifestation of cultural, social and economic processes shaped by the geometry of the natural and man-made world [1]. The complexity of urban forms, similar to that of natural systems, cannot be fully determined by Euclidean geometry. Fractal objects are self-similar through an assemblage of rescaled copies of themselves and when rescaling are either anisotropic or dependent on a direction [5]. These objects or forms are too complex to be described in Euclidean space by topological Cartesian dimensions (1D, 2D or 3D). Instead, they can be characterised by a value of fractal dimension, a statistical concept summarising the degree of self-similarity.
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