An approximative calculation of the fractal structure in self-similar tilings

TL;DR

This paper presents a method to estimate the fractal dimension of self-similar tilings derived from stochastic processes, enabling efficient analysis of fractal structures in networks and urban patterns.

Contribution

It introduces a novel approach to approximate fractal dimensions in self-similar tilings without extensive computations, applicable to various geographical networks.

Findings

Derived size distribution of layered areas in networks

Estimated fractal dimension efficiently using distribution data

Applicable to stochastic self-similar tilings

Abstract

Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the fractal dimension by using the distribution without huge computations. This method can be applied to self-similar tilings based on a stochastic process.