Dimensions of the Boundaries of Self-Similar Sets

DOI10.1080/10586458.2003.10504709zbMath1054.28006OpenAlexW1997118319MaRDI QIDQ4811488

Sze-Man Ngai, Ka-Sing Lau

Publication date: 6 September 2004

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1064858781

zbMATH Keywords

Hausdorff dimensionattractorbox dimensioniterated function systemsIFSself-affine tileself-similar tilecontractive similitudesfinite type conditionfinite boundary type condition

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78) Dimension theory of smooth dynamical systems (37C45)

Related Items (4)

On the boundary of self-affine sets ⋮ Boundaries of disk-like self-affine tiles ⋮ A generalized finite type condition for iterated function systems ⋮ BOX-COUNTING DIMENSION RELATED TO THE BOUNDARY OF HEXAGONAL ARRAYS FOR AN EFFICIENT DIGITAL EARTH MODEL

Cites Work

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• Multifractal measures and a weak separation condition
• The boundaries of self-similar tiles in \(\mathbb{R}^n\)
• Self-affine sets and graph-directed systems
• Self-affine tiles in \(\mathbb{R}^n\)
• HAUSDORFF DIMENSION OF SELF-SIMILAR SETS WITH OVERLAPS
• The Hausdorff Dimension of the Boundary of a Self-Similar Tile
• On the boundary of attractors with non-void interior
• THE BOUNDARY OF THE ATTRACTOR OF A RECURRENT ITERATED FUNCTION SYSTEM

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