A Topological Representation for Taking Cities as a Coherent Whole
Bin Jiang

TL;DR
This paper introduces a topology-based geographic representation of cities as interconnected points within hierarchical networks, enabling analysis of their wholeness and offering new insights for urban design and pattern assessment.
Contribution
It develops a novel topological framework for representing cities as hierarchical networks, contrasting with traditional geometry-based methods, and demonstrates its application through case studies.
Findings
Cities exhibit properties of differentiation and adaptation in their wholeness.
The topological representation effectively captures hierarchical relationships among cities.
Case studies validate the approach using data from China and UK cities.
Abstract
A city is a whole, as are all cities in a country. Within a whole, individual cities possess different degrees of wholeness, defined by Christopher Alexander as a life-giving order or simply a living structure. To characterize the wholeness and in particular to advocate for wholeness as an effective design principle, this paper develops a geographic representation that views cities as a whole. This geographic representation is topology-oriented, so fundamentally differs from existing geometry-based geographic representations. With the topological representation, all cities are abstracted as individual points and put into different hierarchical levels, according to their sizes and based on head/tail breaks - a classification scheme and visualization tool for data with a heavy tailed distribution. These points of different hierarchical levels are respectively used to create Thiessen…
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