scholarly journals Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators

2011 ◽  
Vol 227 (4) ◽  
pp. 1349-1398 ◽  
Author(s):  
Michel L. Lapidus ◽  
Erin P.J. Pearse ◽  
Steffen Winter
Keyword(s):  
Self Similar ◽  
Tube Formulas

TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 349-361 ◽  
Author(s):  
BÜNYAMIN DEMÍR ◽  
ALI DENÍZ ◽  
ŞAHIN KOÇAK ◽  
A. ERSIN ÜREYEN
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Complex Dimensions ◽  
Tubular Neighborhoods ◽  
Self Similar ◽  
Tube Formulas

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.

Tube Formulas for Self-Similar and Graph-Directed Fractals

2013 ◽  
Vol 35 (3) ◽  
pp. 36-49 ◽  
Author(s):  
Ali˙ Deni˙z ◽  
Şahi˙n Koçak ◽  
Yunus Özdemi˙r ◽  
Adem Ersi˙n Üreyen
Keyword(s):  
Self Similar ◽  
Tube Formulas

scholarly journals Tube Formulas and Complex Dimensions of Self-Similar Tilings

2010 ◽  
Vol 112 (1) ◽  
pp. 91-136 ◽  
Author(s):  
Michel L. Lapidus ◽  
Erin P. J. Pearse
Keyword(s):  
Complex Dimensions ◽  
Self Similar ◽  
Tube Formulas

Self-similar collapse with non-radial motions

2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  
Self Similar
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