Self-affine fractals of finite type

Christoph 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 -