ABSTRACT This study of the evolution of urban forms examines the relationship between urban expansion (the enlargement of an urban area) and densification (the increase in the volume of the built form). Densification involves infinitesimally small, dispersed accretions, while the expansion of the urban surface involves the incorporation of larger areas usually on the edge of a city. As a result, built-form density grows steadily to the precise moment when a new urban land is added, when it suddenly falls, only to grow again until a new catastrophe occurs. This paper provides evidence that the size and duration of urban land accretions exhibit power-law distributions for both size and duration, and that the break points that occur when density falls due to new urban land accretion are predictable. These results provide further evidence that urban systems are characterized by self-organized criticality.

中文翻译：

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自组织的关键性和城市形态系统动力学（以巴西城市为参照）

摘要这项关于城市形态演变的研究考察了城市扩张（城市面积的扩大）与致密化（建筑形式体积的增加）之间的关系。致密化涉及极小的分散体，而城市表面的扩张则涉及通常在城市边缘的较大区域的合并。结果，建筑形式的密度稳定地增长到添加新的城市土地时的精确时刻，当它突然下降时，直到再次发生新的灾难之前才再次增长。本文提供的证据表明，城市土地积聚的大小和持续时间在大小和持续时间上都表现出幂律分布，并且可以预测由于新的城市土地积聚导致的密度下降时出现的断点。