  Entropy relates the fast, microscopic behaviour of the elements in a system
to its slow, macroscopic state. We propose to use it to explain how, as
complexity theory suggests, small scale decisions of individuals form cities.
For this, we offer the first interpretation of entropy for cities that reflects
interactions between different places through interdependently linked states in
a multiscale approach. With simulated patterns we show that structural
complexity in spatial systems can be the most probable configuration if the
elements of a system interact across multiple scales. In the case study that
observes the distribution of functions in West London from 1875 to 2005, we can
partly explain the observed polycentric sprawl as a result of higher entropy
compared to spatially random spread, compact mixed use growth or fully
segregated patterns. This work contributes to understanding why cities are
morphologically complex, and describes a consistent relationship between
entropy and complexity that accounts for contradictions in the literature.
Finally, because we evaluate the constraints urban morphology imposes on
possible ways to use the city, the general framework of thinking could be
applied to adjust urban plans to the uncertainty of underlying assumptions in
planning practice.
