Boundary parametrization of self-affine tiles
نویسندگان
چکیده
منابع مشابه
Boundary Parametrization of Planar Self-affine Tiles with Collinear Digit Set
We consider a class of planar self-affine tiles T generated by an expanding integral matrix M and a collinear digit set D as follows :
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A self-affine tile in R is a set T of positive measure with A(T) = d ∈ $ < (T + d), where A is an expanding n × n real matrix with det (A) = m on integer, and $ = {d 1 ,d 2 , . . . , d m } ⊆ R is a set of m digits. It is known that self-affine tiles always give tilings of R by translation. This paper extends the known characterization of digit sets $ yielding self-affine tiles. It proves seve...
متن کاملDisklikeness of Planar Self-affine Tiles
We consider the disklikeness of the planar self-affine tile T generated by an integral expanding matrix A and a consecutive collinear digit set D = {0, v, 2v, · · · , (|q|−1)v} ⊂ Z2. Let f(x) = x2+px+q be the characteristic polynomial of A. We show that the tile T is disklike if and only if 2|p| ≤ |q+2|. Moreover, T is a hexagonal tile for all the cases except when p = 0, in which case T is a s...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2011
ISSN: 0025-5645
DOI: 10.2969/jmsj/06320525