N. Bajorin, T. Chen, C. Emmons, M. Hussein, M. Khalil, P. Mody, B. Steinhurst, A. Teplyaev, Vibrations Modes of 3n-gaskets and Other Fractals, J. Phys. A, 41:1, 2008.

Abstract: We study eigenvalues and eigenfunctions (vibration modes) on the class of self-similar symmetric finitely ramified fractals which includes
\(3n\)-gaskets. We consider such examples as the Sierpinski gasket, a non-p.c.f. analog of the Sierpinski gasket, the Level-3 Sierpinski gasket, a fractal 3-tree, the Hexagasket, and one dimensional fractals. We develop a theoretical matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly. We support our theoretical analysis by symbolic and numerical computations.