Asymptotic formula on average path length of fractal networks modeled on Sierpinski gasket

Sandpile model on the Sierpinski gasket fractal.

We investigate the sandpile model on the two-dimensional Sierpinski gasket fractal. We find that the model displays interesting critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes, and topplings and calculate the associated critical exponents t51.5160.04, a51.6360.04, and m51.3660.04. The avalanche size distribution shows power-law behavior modulated by lo...

Localization in fractal spaces: Exact results on the Sierpinski gasket.

Localization due to space structure, rather than due to randomness, is investigated by studying the usual tight-binding model on the Sierpinski gasket. Some exact results are obtained from the decimation —renormalization-group method. It is surprising that there exist an infinite number of extended states on the Sierpinski gasket. This set of extended states forms a Cantor set. The rest of the ...

Sampling on the Sierpinski Gasket

Nanoassembly of a fractal polymer: a molecular "Sierpinski hexagonal gasket".

Mathematics and art converge in the fractal forms that also abound in nature. We used molecular self-assembly to create a synthetic, nanometer-scale, Sierpinski hexagonal gasket. This nondendritic, perfectly self-similar fractal macromolecule is composed of bis-terpyridine building blocks that are bound together by coordination to 36 Ru and 6 Fe ions to form a nearly planar array of increasingl...

Random walks on the Sierpinski Gasket

The generating functions for random walks on the Sierpinski gasket are computed. For closed walks, we investigate the dependence of these functions on location and the bare hopping parameter. They are continuous on the infinite gasket but not differentiable. J. Physique 47 (1986) 1663-1669 OCTOBRE 1986, Classification Physics Abstracts 05.40 05.50 1. Preliminaries and review of known results. C...