Differential Equations on the Sierpinski Gasket

Welcome to the Differential Equatoins on the Sierpinski Triangle website.  This page was created by Jeremy Stanley from Wichita State University. The research presented was created by a collaborative effort between Jeremy Stanley, Bob Strichartz and Alexander Tuplyaev at the Cornell REU program during the summer of 2000.  This page is intended to serve as a reference for further work done on this topic. I include mathematical proofs, explanations of algorithms, and actual code. All of the files are directory structures in .tar format, which can be uncompressed in a Unix/Linux environment. Windows versions should be available soon.
 

Latex

• A general overview of my research, these were the slides used in my final presentation at Cornell.
•  A brief paper on the equipartition of energy for harmonic functions and self-similar Dirichlet forms.

Maple

•  The equipartion of energy
•  The identity for the conductance, and its taylor expansion
•  The identity satisfied by the normal derivative at the boundary
•  The harmonic extension algorightm for elliptic equations, and some explorations of the laplacians (unfinished)

Matlab

•  Numerically approximate solutions to elliptic equations.
•  Numerically approximate the conductance for elliptic equations with 1/a harmonic.
•  Simple algorithm to plot the pentagasket by representing it on the integer lattice using sparse matrices.

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Additions, Corrections or Feedback on this page to:

jeremystan@kscable.com

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Last Update: August 11, 2000