Allometry in the Syntax of Street Networks: Evolution of Adriatic and Ionian Coastal Cities 1800–2010

Abstract

Urban growth is discussed according to the impact of size on metric and topological space syntax measures that describe street networks. The quantitative analysis of three historical stages of cities on the Adriatic and Ionian coastline is supported by a unique database of historical maps and axial map representations. The empirical evidence demonstrates strong and significant allometric relationships of total length of lines to the area of urbanized territory, and total length, total connectivity, overall depth, total choice (betweenness), and total depth entropy to axial map size. In this paper allometric equations are derived for the measures and it is shown that comparative analysis based on means of measures traditionally used in space syntax does not comply with the observed ontogenetic relationships. The allometric trends of length to area and of connectivity to network size are shown to have sublinear scaling exponents, whereas allometric relationships of length, depth, choice, and entropy to network size are expressed with superlinear exponents. The comparison among three historical stages shows that allometry of depth to axial map size maintains statistical equivalence at the ontogenetic scale that transcends various types of street patterns, growth models, and physiographic conditions. In contrast, allometric relationships of depth, choice, and entropy to size reveal distinct universality classes between cities on the Italian and Balkan coasts, and between cities with and without gridiron street patterns.