An IFS for the Stretched Level-n Sierpinski Gasket

Abstract

Broadly, fractals are sets that exhibit a repeating pattern at multiple scales. One important fractal set is the Sierpinski Gasket (SG) which is made up of nested equilateral triangles. A variation of the classic Sierpinski gasket is to create n-levels with the equilateral triangles. Another variation is to stretch the points of intersection for the triangles in SG into line segments of length 0 < α < 1/3. When one combines these variations, one arrives at the stretched level-n Sierpinski gaskets (SSGn) which are the focus of this work. We give an introduction to iterated function systems (IFS) and determine an IFS which generates SSG3. We then describe how one can acquire the IFS for SSGn in general, and conclude with a theorem which determines the Hausdorff dimension for SSGn.