The Beauty of the Symmetric Sierpinski Relatives
Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture
Pages 163–170
Regular Papers
Abstract
The Sierpinski relatives form a fascinating class of fractals because they all possess the same fractal dimension but can have different topologies. The famous Sierpinski gasket is one of these relatives. There is a subclass consisting of symmetric relatives that are particularly beautiful. This paper presents an exploration of these relatives. These eight relatives are all fractal, however their convex hulls are polygons with at most eight sides. The convex hulls provide a way to tile the relatives to obtain other beautiful fractals. The fractals include gasket fractals and fractal frieze patterns.