ABSTRACT

A reptile in the plane is a compact set with non-empty interior that is made up of finitely many congruent tiles. In this chapter, we present a concise summary of existing general methods to obtain connected fractal reptiles with holes for any even integer n ≥ 4 and construct new examples of n − reptile with holes involving reflections and rotations. We also consider some variations of these reptiles and self-similar fractals as special cases and examples of reptiles with holes using integer matrices.