27 research outputs found
Vibration Spectra of the -Tree Fractal
We introduce a family of post-critically finite fractal trees indexed by the
number of branches they possess. Then we produce a Laplacian operator on graph
approximations to these fractals and use spectral decimation to describe the
spectrum of the Laplacian on these trees. Lastly we consider the behavior of
the spectrum as the number of branches increases.Comment: 21 pages, 4 figure