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Entropy 2012, 14(4), 800-833; doi:10.3390/e14040800

Entropies and Scaling Exponents of Street and Fracture Networks

1 UCL Department of Geography, University College London, 1-19 Torrington Place, Gower Street, London WC1E 7HB, UK 2 Department of Earth Sciences, Queen’s Building, Royal Holloway University of London, Egham TW20 0EX, UK
* Author to whom correspondence should be addressed.
Received: 23 March 2012 / Revised: 7 April 2012 / Accepted: 10 April 2012 / Published: 19 April 2012
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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 (R2 = 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, (R2 = 0.845–0.906 for streets, R2 = 0.927 for fractures).
Keywords: street networks; fracture networks; power laws; scaling exponents; entropy street networks; fracture networks; power laws; scaling exponents; entropy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Mohajeri, N.; Gudmundsson, A. Entropies and Scaling Exponents of Street and Fracture Networks. Entropy 2012, 14, 800-833.

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