Falconer's formula for the Hausdorff dimension of a self-affine set in R2
1995 ◽
Vol 15
(1)
◽
pp. 77-97
◽
Keyword(s):
Let A1, A2,…,Ak be a finite set of contractive, affine, invertible self-mappings of R2. A compact subset Λ of R2 is said to be self-affine with affinitiesA1, A2,…,Ak ifIt is known [8] that for any such set of contractive affine mappings there is a unique (compact) SA set with these affinities. When the affine mappings A1, A2,…,Ak are similarity transformations, the set Λ is said to be self-similar. Self-similar sets are well understood, at least when the images Ai(Λ) have ‘small’ overlap: there is a simple and explicit formula for the Hausdorff and box dimensions [12, 10]; these are always equal; and the δ-dimensional Hausdorff measure of such a set (where δ is the Hausdorff dimension) is always positive and finite.
Keyword(s):
2019 ◽
Vol 40
(12)
◽
pp. 3217-3235
◽
2009 ◽
Vol 29
(1)
◽
pp. 201-221
◽
2008 ◽
Vol 28
(5)
◽
pp. 1635-1655
◽
1985 ◽
Vol 26
(2)
◽
pp. 115-120
◽
2004 ◽
Vol 56
(3)
◽
pp. 529-552
◽
Keyword(s):
Keyword(s):