Dynamics of a Vicsek fractal: The boundary effect and the interplay among the local symmetry, the self-similarity, and the structure of the fractal

The role of the boundary condition on the transverse vibrations of an nth-stage Vicsek fractal as n{→}{∞} was studied using nearest-neighbor interactions. Our findings indicate that, although the interplay among the local symmetry, the self-similarity, and the structure is the underlying reason for the unusual properties of the Vicsek fractal, the boundary condition has definitely left its imprint on almost every feature of the dynamics of the system.