Welcome to Singularities at Periodic Points of the Sierpinski Gasket. This website was created by Abby Shaw-Krauss from UCLA for the Cornell Math REU 2003 program. Here I have a discussion of my work and some results and Maple code for further use.

My research this summer focused on the singularites in functions on Sierpinski Gasket (SG). This gasket is an infinite point set constructed by taking the three vertices of an equilateral triangle and creating a smaller (upside-down) equilateral triangle from the midpoints of the original. This process continues infintely using the resulting three (right-side-up) triangles. However, I only worked on finite levels or graph approximations of the SG. A cell is a subset of certain graph.

Following up on previous research in the area, I considered harmonic functions on the SG. From here I created multiharmonic functions. These are the most basic functions to work with and are the basis for power series.

For background information on continuous functions on the SG see Jonathan Needleman's site. For research on singularities at boundary points of the SG see Nitsan Ben-Gal's site.