Abstract
Let A be an expanding integer n×n matrix and D be a finite subset of Zn. The self-affine set T=T(A,D) is the unique compact set satisfying the equality A(T)=∪dD(T+d). We present an effective algorithm to compute the Lebesgue measure of the self-affine set T, the measure of the intersection T∩(T+u) for u∈Zn, and the measure of the intersection of self-affine sets T(A,D1)∩T(A,D2) for different sets D1, D2⊂Zn.
Original language | English (US) |
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Pages (from-to) | 389-393 |
Number of pages | 5 |
Journal | Discrete and Computational Geometry |
Volume | 46 |
Issue number | 2 |
DOIs | |
State | Published - Sep 2011 |
Funding
R.V. Kravchenko was partially supported by NSF grant 0503688.
Keywords
- Graph-directed system
- Self-affine set
- Self-similar action
- Tile
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics