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A Class of Self-Similar Fractals with Overlap Structure

✍ Scribed by Hui Rao; Zhi-Ying Wen

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
237 KB
Volume
20
Category
Article
ISSN
0196-8858

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✦ Synopsis

For the contracting similarities S x s xr3, S x s xq r3, and S x s 1 2 3 Ž . w x xq2 r3, where g 0, 1 , let F denote the invariant set with respect to S , S , 1 2 and S . In this paper, we study the Hausdorff measure, Hausdorff dimension, and 3 w x Ž . the structure of F . Let s bra g ‫ޑ‬ l 0, 1 , a, b s 1. Using combinatorial < < Ž . techniques, we show that F ) 0 if a ' b k 0 mod 3 ; otherwise, F is a Cantorlike fractal with recursive construction.

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