Entropy, complexity, and spatial information

Michael Batty (), Robin Morphet (), Paolo Masucci () and Kiril Stanilov ()

Journal of Geographical Systems, 2014, vol. 16, issue 4, 363-385

Abstract: We pose the central problem of defining a measure of complexity, specifically for spatial systems in general, city systems in particular. The measures we adopt are based on Shannon’s (in Bell Syst Tech J 27:379–423, 623–656, 1948 ) definition of information. We introduce this measure and argue that increasing information is equivalent to increasing complexity, and we show that for spatial distributions, this involves a trade-off between the density of the distribution and the number of events that characterize it; as cities get bigger and are characterized by more events—more places or locations, information increases, all other things being equal. But sometimes the distribution changes at a faster rate than the number of events and thus information can decrease even if a city grows. We develop these ideas using various information measures. We first demonstrate their applicability to various distributions of population in London over the last 100 years, then to a wider region of London which is divided into bands of zones at increasing distances from the core, and finally to the evolution of the street system that characterizes the built-up area of London from 1786 to the present day. We conclude by arguing that we need to relate these measures to other measures of complexity, to choose a wider array of examples, and to extend the analysis to two-dimensional spatial systems. Copyright The Author(s) 2014

Keywords: Information; Entropy; Density; Spatial complexity; London population; London street system; C46; R12; R14; R40; R52 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (14)

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DOI: 10.1007/s10109-014-0202-2

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