Fractal Tiles and Quasidisks

Da-Wen Deng, Xiangtan University
Sze-Man Ngai, Georgia Southern University

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.