Fractal Rep Tiles of ℝ2 and ℝ3 Using Integer Matrices

Abstract

This paper is devoted to the study of self-similar fractal rep tiles of the Euclidean planes [Formula: see text] and [Formula: see text] using integer matrices. We construct many examples appearing in the literature, as well as new examples by integer matrices. Several exotic and radially symmetric self-similar rep tiles and their variations are obtained with change of bases extending the work by Bandt and others. We also present a few examples of polyhedral self-similar rep tiles including variations.

Fractals: An Eclectic Survey, Part-I

“…Computer generated drawings of tilings of the plane by self-similar fractal rep tiles appeared in the papers beginning 1980s and 1990s, for example the lattice tiling of the plane by copies of the twindragon. We refer to the works of several authors [23][24][25][26][27][28][29][30][31] for the study of fractal rep tiles.…”