Representing Geographic Space as a Hierarchy of Recursively Defined Subspaces for Computing the Degree of Order

TL;DR

This paper introduces a novel organic hierarchical representation of geographic space based on recursive subspaces to quantify the degree of order, or 'living structure,' with applications in urban environments and implications for geographic science.

Contribution

It develops a new organic, hierarchical approach to representing geographic space, contrasting with conventional mechanical models, and introduces methods to compute the space's degree of order.

Findings

Successfully applied to urban environments, patterns, and black-white strips

Demonstrated advantages over traditional geographic representations

Linked the degree of order to concepts like beauty and coherence

Abstract

As Christopher Alexander discovered, all space or matter - either organic or inorganic - has some degree of order in it according to its structure and arrangement. The order refers to a kind of structural character, called living structure, which is defined as a mathematical structure that consists of numerous substructures with an inherent hierarchy. Across the hierarchy, there are far more small substructures than large ones, while on each level of the hierarchy the substructures are more or less similar in size. In this paper we develop a new approach to representing geographic space as a hierarchy of recursively defined subspaces for computing the degree of order. A geographic space is first represented as a hierarchy of recursively defined subspaces, and all the subspaces are then topologically represented as a network for computing the degree of order of the geographic space, as well as that of its subspaces. Unlike conventional geographic representations, which are mechanical in nature, this new geographic representation is organic, conceived, and developed under the third view of space; that is, space is neither lifeless nor neutral, but a living structure capable of being more living or less living. Thus, the order can also be referred to as life, beauty, coherence, or harmony. We applied the new representation to three urban environments, 253 patterns, and 35 black-white strips to verify it and to demonstrate advantages of the new approach and the new kind of order. We further discuss the implications of the approach and the order on geographic information science and sustainable urban planning. Keywords: Living structure, pattern language, life, wholeness, coherence, structural beauty