TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS

Author:

DEMÍR BÜNYAMIN1,DENÍZ ALI1,KOÇAK ŞAHIN1,ÜREYEN A. ERSIN1

Affiliation:

1. Department of Mathematics, Science Faculty, Anadolu University, Yunusemre Campus, Tepebaşı 26470, Eskişehir, Turkey

Abstract

Lapidus and Pearse proved recently an interesting formula about the volume of tubular neighborhoods of fractal sprays, including the self-similar fractals. We consider the graph-directed fractals in the sense of graph self-similarity of Mauldin-Williams within this framework of Lapidus-Pearse. Extending the notion of complex dimensions to the graph-directed fractals we compute the volumes of tubular neighborhoods of their associated tilings and give a simplified and pointwise proof of a version of Lapidus-Pearse formula, which can be applied to both self-similar and graph-directed fractals.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modelling and Simulation

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