Entropies and scaling exponents of street and fracture networks

Abstract

Many natural and man-made lineaments form networks that can be analysed through entropy and energy considerations. Here we report the results of a detailed study of the variations in trends and lengths of 1554 named streets and 6004 street segments, forming a part of the evolving street network of the city of Dundee in East Scotland. Based on changes in the scaling exponents (ranging from 0.24 to 3.89), the streets can be divided into 21 populations. For comparison, we analysed 221 active crustal fractures in Iceland that (a) are of similar lengths as the streets of Dundee; (b) are composed of segments; and (c) form evolving networks. The streets and fractures follow power-law size distributions (validated through various statistical tests) that can be partly explained in terms of the energies needed for their formation. The entropies of the 21 street populations and 9 fracture populations show strong linear correlations with (1) the scaling exponents (R 2 = 0.845-0.947 for streets, R2 = 0.859 for fractures) and with (2) the length ranges, that is, the differences between the longest and shortest streets/fractures, (R 2 = 0.845-0.906 for streets, R 2 = 0.927 for fractures). © 2012 by the authors.