## Fractals

### A Brief Description

We have studied the Vibrational dynamics of an infinite Vicsek fractal using the Real Space Green's Function method and the decimation technique. The vibrational properties of a Vicsek fractal reveals interesting features which arise from an interplay of self-similarity, 4-fold local symmetry, and the tree-like nature of the Vicsek fractal. The most intriguing feature is the side-by-side occurence of localized and extended states. This feature is very different from a truly disordered system in 3D, where exists a clear demarcation between extended and localized states.

### Recent Publications in Fractals

- S.Y. Wu, J.A. Cocks and C.S. Jayanthi,
*A Real Space Green's Function Approach to the Dynamics of a Vicsek Fractal*, Physical Review Letters,**69**, 1955 (1992). - C.S. Jayanthi and S.Y. Wu,
*Frequency Spectrum of a General Vicsek Fractal*, Physical Review B**48**, 10188 (1993). - C.S. Jayanthi and S.Y. Wu,
*Exact Calculation of the Dynamics of a General Vicsek Fractal*, Physical Review B**48**10199 (1993). - C.S. Jayanthi and S.Y. Wu,
*Effects of Free-End Boundary Condition on the Frequency Spectrum of a Vicsek Fractal*, S.Y. Wu and C.S. Jayanthi,*Fractals*,**1**, 922, (1993). - C.S. Jayanthi and S.Y. Wu,
*Dynamics of a Vicsek Fractal: The Boundary Effect and the Interplay among the Local Symmetry, the Self-Similarity, and the Structure of the Fractal*, Phys. Rev. B**50**, 897 (1994).