Fractal Tiles and Quasidisks

Da Wen Deng; Sze Man Ngai

doi:10.1007/s00209-014-1372-9

Fractal Tiles and Quasidisks

Da Wen Deng, Sze Man Ngai

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that the interiors of a large class of planar disklike self-similar tiles are quasidisks. We also show that in general, the interior of a disklike self-affine tile may not be a John domain and thus may not be a quasidisk.

Original language	American English
Journal	Mathematische Zeitschrift
Volume	279
DOIs	https://doi.org/10.1007/s00209-014-1372-9
State	Published - Feb 1 2015

Keywords

John domain
Linearly connected domain
Quasidisk
Self-affine tile
Self-similar tile

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Education
Mathematics

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http://dx.doi.org/10.1007/s00209-014-1372-9

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title = "Fractal Tiles and Quasidisks",

abstract = "We show that the interiors of a large class of planar disklike self-similar tiles are quasidisks. We also show that in general, the interior of a disklike self-affine tile may not be a John domain and thus may not be a quasidisk.",

keywords = "John domain, Linearly connected domain, Quasidisk, Self-affine tile, Self-similar tile",

author = "Deng, {Da Wen} and Ngai, {Sze Man}",

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AU - Deng, Da Wen

AU - Ngai, Sze Man

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2014.

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Y1 - 2015/2/1

N2 - We show that the interiors of a large class of planar disklike self-similar tiles are quasidisks. We also show that in general, the interior of a disklike self-affine tile may not be a John domain and thus may not be a quasidisk.

AB - We show that the interiors of a large class of planar disklike self-similar tiles are quasidisks. We also show that in general, the interior of a disklike self-affine tile may not be a John domain and thus may not be a quasidisk.

KW - John domain

KW - Linearly connected domain

KW - Quasidisk

KW - Self-affine tile

KW - Self-similar tile

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/305

UR - http://dx.doi.org/10.1007/s00209-014-1372-9

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DO - 10.1007/s00209-014-1372-9

M3 - Article

SN - 0025-5874

VL - 279

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

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Fractal Tiles and Quasidisks

Abstract

Keywords

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