Spectral Operators on Vicsek Sets

Denglin Zhou proved in his thesis that a class of fractals called Vicsek sets admit spectral decimation, an algorithm for recursively constructing eigenfunctions of a Laplacian operator. This page displays work done at the summer 2008 Cornell REU. During a summer 2008 Cornell math REU we implemented spectral decimation in MATLAB and used it to investigate eigenvalues, eigenfunctions, and spectral operators:

Our MATLAB code (tar.gz | zip). Our paper on arXiv.

Send any comments/suggestions to: mhw33@cornell.edu

Additional acknowledgements: Steven Heilman, Yingying Chan, Taryn Flock, Steve Gaarder, Bob Strichartz, Russ Thompson

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Last Update: March 30, 2009