Self-Organisation in Spatial Systems—From Fractal Chaos to Regular Patterns and Vice Versa

Abstract

This study offers a new perspective on the evolutionary patterns of cities or urban agglomerations. Such developments can range from chaotic to fully ordered. We demonstrate that in a dynamic space of interactive human behaviour cities produce a wealth of gravitational attractors whose size and shape depend on the resistance of space emerging inter alia from transport friction costs. This finding offers original insights into the complex evolution of spatial systems and appears to be consistent with the principles of central place theory known from the spatial sciences and geography. Our approach is dynamic in nature and forms a generalisation of hierarchical principles in geographic space.

Blessing in disguise: long-run benefits of urban disasters

“…This phenomenon has prompted an avalanche of studies on non-linear dynamics in complex spaces (see Reggiani and Nijkamp 2009), which may exhibit various dynamic evolutionary pathways (e.g., a cusp catastrophe), depending on initial conditions and transition dynamics. Sometimes, very complicated -even fractal -movements in spatial systems may occur in complex multi-agent systems (see, e.g., Banaszak et al 2015). Clearly, both natural and human-made systems may exhibit a wealth of dynamic behaviour, especially in those cases where human responses intervene with natural systems (e.g., in the case of climate change).…”

Invariant Patterns for Replicator Dynamics on a Hexagonal Lattice

“…The distributions of satellite cities, towns, and villages around Berlin and London were shown to follow a universal law [Makse et al, 1995]. Self-organization in spatial systems was studied [Banaszak et al, 2015] and a group-theoretic spectrum analysis of self-organization patterns of city distribution in Southern Germany and Eastern USA was conducted [Ikeda et al, 2018d].…”

Group-Theoretic Spectrum Analysis of Population Distribution in Southern Germany and Eastern USA

“…1(b)]. Several attempts to simulate the self-organization of central place systems have been conducted through modeling of economic mechanisms of agglomerations [Eaton & Lipsey, 1975;Munz & Weidlich, 1990;Tabuchi & Thisse, 2011;Banaszak et al, 2015]. Yet scientific verification of the existence of hexagonal agglomerations in the real world has been lacking over the years.…”