TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, vol.18, no.3, pp.349-361, 2010 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 18 Issue: 3
- Publication Date: 2010
- Doi Number: 10.1142/s0218348x10004919
- Journal Name: FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.349-361
- Keywords: Graph-Directed Fractals, Graph Self-Similarity, Tube Formula, Complex Dimensions, Steiner Formula, Self-Similar Tiling, Zeta Functions
- Anadolu University Affiliated: Yes
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.