Symmetries on self-similar fractals

Abstract

This thesis discusses self-similar fractals, more specifically different symmetries on self-similar fractals. We build the fractal space as a collection of compact subsets of a complete metric space. Further, we add IFS theory to give the foundation to what fractals are and how they are constructed. We also use IMS’s to represent the fractals. We will investigate the Sierpinski gasket and the Vicsek fractal, two different fractals that is shown to have two different outcomes. We find that the Sierpinski gasket fall under the same symmetry group as the equilateral triangle, however the Vicsek fractal does not fall under the same symmetry group as the square.