‘Compactness’ in Zoning: the circle as the ideal.

I saw a thought provoking presentation recently, given by Wenwen Li of the University of California Santa Barbara, the talk was a wide ranging insight into Cyber Infrastructure, its uses for geospatial information, and some of the computational techniques that underpinned the project. One element of the project involved zone design for the greater Los Angeles region, and involved the implementation of an algorithm that was intended to aggregate small areal units into larger zones whilst meeting a number of conditions, principle among these conditions was ‘compactness’. The output looked very much like a single hierarchy of Christaller hexagons, and this got me thinking about the nature of space and compactness.

Christaller’s hexagons are the defining illustration of something called ‘central place theory’, a geographical abstraction that idealises settlement pattern based upon an underlying space which is assumed to be isotropic. The assumption of spatial isotropy is the big leap in this model, it assumes that the ‘friction of distance’ from any given point increases at an equal rate whichever way you go from that point. Clearly such a suggestion is not applicable to Los Angeles, where huge freeways and interchanges can make adjacent parcels of land remote neighbours, and increase the connection between advantageously placed non-adjacent sites? Surely a city in which sprawl and ribbon development, as well as segregated communities should be modeled differently? Why then do many of our zoning algorithms favour compact ‘circular’ shapes, very much in the christaller mould, and why do we reject uncompact areal features as ugly slivers? In short, how did the circle come to be the ideal shape of zone in regional studies? Certainly, it is easier, both implementationally and conceptually, to model circles than to consider optimising a zone system over an n zone by n zone similarity matrix pertaining to variables which may be important to aggregating any set of areal units. However, as we explore more and more the complex systems defined by cities and regions, surely there is a need to start integrating a more realistic anisotropic view of space, one in which the friction of distance from any given point in any given direction is defined by the underlying demography, built environment and/or infrastructure.

One such attempt at this, AMOEBA (A Multidirectional Optimum Ecotope-Based Algorithm), developed by Aldstadt and Getis, is worth noting. In this algorithm, zones are defined via the Getis-Ord Gi* statistic, which is a local statistic for identifying clustering, thus zones are defined by local conditions, which are free to vary anistropically across space, rather than by a predefined preference for circles. Spectacularly this algorithm is implemented in the superb clusterpy python module for spatially constrained clustering.