The Projective Octagasket
A compilation of work done on the Projective Octagasket
2017 Cornell SPUR Program
Yiran Mao
Levente Szabo
Robert Strichartz
Wing Hong Wong
A compilation of work done on the Projective Octagasket
2017 Cornell SPUR Program
Yiran Mao
Levente Szabo
Robert Strichartz
Wing Hong Wong
The existence of a self similar Laplacian on the Projective Octagasket, a non-finitely ramified fractal is only conjectured. We present experimental results using a cell approximation technique originally given by Kusuoka and Zhou. A rigorous recursive algorithm for the discrete Laplacian is given. Further, the spectrum and eigenfunctions of the Laplacian together with its symmetries are categorized and utilized in the construction of solutions to the heat equation.
Here we give a brief introduction to the construction of the Projective Octagasket and an approximation to its Laplacian. For details concerning our algorithms and results please download our paper.
Download
Our Matlab files were used in constructing the Projective Octagasket, estimating its Laplacian, finding the eigenvalues and eigenvectors of its Laplacian and approximations to the heat kernel.
Our data includes spreadsheets of all eigenvalues, heat kernel and distance matrices. Also images are included portraying the eigenfunctions of the Laplacian.