# Spatial Point Pattern and Urban Morphology: Perspectives from Entropy, Complexity and Networks

## TL;DR

This paper introduces a novel framework using entropy maximisation to quantify and compare urban spatial patterns across different cities, revealing diverse morphological types linked to geography and development.

## Contribution

It proposes a new entropy-based method to characterize urban spatial patterns through three length scales and two decoherence measures, enabling city comparisons.

## Key findings

- Different urban morphologies correlate with geographical background.
- The framework effectively distinguishes cities based on spatial pattern metrics.
- Urban development status influences the spatial arrangement of locations.

## Abstract

Spatial organisation of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding various aspects of the system. In this work, a framework to characterise the spatial pattern of urban locations based on the idea of entropy maximisation is proposed. Three spatial length scales in the system with discerning interpretations in terms of the spatial arrangement of the locations are calculated. Using these length scales, two quantities are introduced to quantify the system's spatial pattern, namely mass decoherence and space decoherence, whose combination enables the comparison of different cities in the world. The comparison reveals different types of urban morphology that could be attributed to the cities' geographical background and development status.