Sierpinski Gasket Approximations and Ternary Colorings
Tara Taylor

Proceedings of Bridges 2025: Mathematics and the Arts
Pages 301–308
Regular Papers

Abstract

This paper presents a way to connect approximations of the Sierpinski gasket with colorings of ternary strings. One way to model the gasket is with an iterated function system (IFS) that consists of three contractive mappings. An approximation is obtained by applying the contractive maps a finite numbers of times to some initial object. The gasket is the limit of these approximations. A finite address in the form of a ternary string corresponds to a finite composition of the contractive mappings. The Sierpinski arrowhead curve is another model for the gasket, and we can use it to provide an ordering of ternary strings that is different from the standard ordering. We present a way to associate a ternary string with a color from the CMY color model. Colored approximations can be used to create Sierpinski color sequences.

Files