This page contains the results and programs of a Research Experience for Undergraduates (REU) program held at Cornell University, summer 2006. Work for this project was done by Stacey Goff (stacey.goff@ncf.edu) under the direction of Dr. Robert Strichartz (str@math.cornell.edu) as part of ongoing research in analysis of fractals. The project involved approximating the Neumann spectrum on non-Post Critically Finite (PCF) fractals using the outer approximation method, as well as eigenfunction calculations including looking at heat kernels and Dirichlet kernels. For more information on the ideas behind the research, take a look at the 'theoretical' page.
The image is a Neumann eigenfunction of the Laplacian on an approximation to the Sierpinski carpet. For other images related to this research, see the 'images' page, and for information about doing similar calculations and generating images using MATLAB, see the 'programs' page.