# Self-affine fractals of finite type

Christoph Bandt; Mathias Mesing

Banach Center Publications (2009)

- Volume: 84, Issue: 1, page 131-148
- ISSN: 0137-6934

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topChristoph Bandt, and Mathias Mesing. "Self-affine fractals of finite type." Banach Center Publications 84.1 (2009): 131-148. <http://eudml.org/doc/281970>.

@article{ChristophBandt2009,

abstract = {In the class of self-affine sets on ℝⁿ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which decides whether the tile is homeomorphic to a disk.},

author = {Christoph Bandt, Mathias Mesing},

journal = {Banach Center Publications},

keywords = {self-affine set; finite type fractal; tile},

language = {eng},

number = {1},

pages = {131-148},

title = {Self-affine fractals of finite type},

url = {http://eudml.org/doc/281970},

volume = {84},

year = {2009},

}

TY - JOUR

AU - Christoph Bandt

AU - Mathias Mesing

TI - Self-affine fractals of finite type

JO - Banach Center Publications

PY - 2009

VL - 84

IS - 1

SP - 131

EP - 148

AB - In the class of self-affine sets on ℝⁿ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which decides whether the tile is homeomorphic to a disk.

LA - eng

KW - self-affine set; finite type fractal; tile

UR - http://eudml.org/doc/281970

ER -

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