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Self-organisation in territories leads to the emergence of patterns in urban systems that shape the interactions between cities, resulting in a hierarchical organisation. Governance follows as well a hierarchical structure, breaking the…
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe…
In this chapter, we discuss urban mobility from a complexity science perspective. First, we give an overview of the datasets that enable this approach, such as mobile phone records, location-based social network traces, or GPS trajectories…
The shape of buildings plays a critical role in the energy efficiency, lifestyles, land use and infrastructure systems of cities. Thus, as most of the world's cities continue to grow and develop, understanding the interplay between the…
Urban morphology, examining city spatial configurations, links urban design to sustainability. Morphology metrics play a fundamental role in performance-driven computational urban design (CUD) which integrates urban form generation,…
Understanding demographic and migrational patterns constitutes a great challenge. Millions of individual decisions, motivated by economic, political, demographic, rational, and/or emotional reasons underlie the high complexity of…
Benchmarking and monitoring urban design and transport features is critical to achieving local and international health and sustainability goals. However, most urban indicator frameworks use coarse spatial scales that only allow…
Complex networks provide a means to describe cities through their street mesh, expressing characteristics that refer to the structure and organization of an urban zone. Although other studies have used complex networks to model street…
The shape of urban settlements plays a fundamental role in their sustainable planning. Properly defining the boundaries of cities is challenging and remains an open problem in the Science of Cities. Here, we propose a worldwide model to…
Increasing evidence suggests that cities are complex systems, with structural and dynamical features responsible for a broad spectrum of emerging phenomena. Here we use a unique data set of human flows and couple it with information on the…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
A substantial share of the Earth's land surface is managed by humans, with cities representing the most extreme form of anthropogenic land use. There are zillion ways in which settlements can be arranged across a given area, and their…
Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark's model…
Green areas are a crucial element in evolution of a city, contributing to improve citizens' life, to reduce effects of climate change, and to make possible the survival of other species in urban areas. Unfortunately, the above effects are…
The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban…
We study a stochastic model of urban growth generating spatial distributions of population densities at an intermediate mesoscopic scale. The model is based on the antagonist interplay between the two opposite abstract processes of…
Human mobility is a fundamental process underpinning socioeconomic life and urban structure. Classic theories, such as egocentric activity spaces and central place theory, provide crucial insights into specific facets of movement, like…
Understanding the high-order relationship between urban form and function is essential for modeling the underlying mechanisms of sustainable urban systems. Nevertheless, it is challenging to establish an accurate data representation for…
Quantifying the topological similarities of different parts of urban road networks (URNs) enables us to understand the urban growth patterns. While conventional statistics provide useful information about characteristics of either a single…
With the rise of geospatial big data, new narratives of cities based on spatial networks and flows have replaced the traditional focus on locations. While plenty of research have empirically analyzed network structures, there lacks a…