An Approximative Calculation of the Fractal Structure in Self-Similar Tilings

Yukio HAYASHI 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E94-A  No.2  pp.846-849
Publication Date: 2011/02/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Nonlinear Problems
Keyword: 
complex network science,  geographical network,  random fractal,  Markov chain,  urban planning, 

Full Text: PDF

Summary: 
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.