BOUNDARY DIMENSIONS OF FRACTAL TILINGS

Abstract

A fractal tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. In this paper, we investigate the boundary dimension of [Formula: see text]- and [Formula: see text]-tilings. We first derive an explicit recursion formula for the boundary edges of [Formula: see text]- and [Formula: see text]-tilings. Then we present an analytical expression for their fractal boundary dimensions using matrix methods. Results indicate that, as [Formula: see text] increases, the boundaries of [Formula: see text]- and [Formula: see text]-tilings will degenerate into general Euclidean curves. The method proposed in this paper can be extended to compute the boundary dimensions of other kinds of fractal tilings.