Spatial rules that generate urban patterns: Emergence of the power law in the distribution of axial line length

This paper studies emergence/generation of power law in rank-order distribution of axial line length, which is a global pattern observed in real cities, due to interaction of a set of seven simple spatial rules at a local scale. These rules and their interactions form a model expected to simulate the morphological structure of free spaces in unplanned organic pedestrian small cities. Effects of each of the seven rules are discussed through repeated simulations of eight possible combinations of the rules, using a bottom-up process. The results show that the rules generate environments with statistically stable rank-order distribution of axial line length that follows the power law. It means that the axial maps of the simulated environments have a scale-free hierarchical structure such that their distributions lean toward short axial lines. It also represents dominance of local spatial structure, as the model renders a faster rate of growth at a local scale while allowing a steady growth at a global scale.