Showing papers on "n-flake published in 1997"
TL;DR: By forming a sequence of coverings of the Sierpinski gasket, a descending sequence of the upper limits of Hausdorff measure is obtained in this paper, which is the best upper limit known so far.
Abstract: By forming a sequence of coverings of the Sierpinski gasket, a descending sequence of the upper limits of Hausdorff measure is obtained. The limit of the sequence is the best upper limit of the Hausdorff measure known so far.
20 citations
TL;DR: In this paper, it was shown that the mean walklength of a random walker on a Menger sponge of N sites, with coordination number ν = 4 and fractal dimension d ∼ 2.7268, is intermediate between results calculated for walks on the corresponding N = l × m torus (ν = 4, d = 2) and the d = 3 simple cubic lattice.
15 citations
TL;DR: In this article, a variety of fractal-based dynamical systems with fractal geometry can be constructed, including the Sierpinski gasket, the Cantor set, and lattices of these fractal based structures.
Abstract: Dynamical systems with fractal geometry can be constructed in a variety of ways: We illustrate this variety with examples based on the Cantor set, the Sierpinski gasket, and on lattices of these fractal-based structures. Depending on the physical parameters, the models can exhibit both discrete and continuous spectra.
6 citations
TL;DR: In this article, an iteration rule for real numbers capable of generating attractors with dragon-, snowflake-, sponge-, or Swiss flag-like cross sections is introduced. The idea behind it is the mapping of a torus into two (or more) shrunken and twisted tori located inside the previous one.
Abstract: We introduce an iteration rule for real numbers capable to generate attractors with dragon-, snowflake-, sponge-, or Swiss-flag-like cross sections. The idea behind it is the mapping of a torus into two (or more) shrunken and twisted tori located inside the previous one. Three distinct parameters define the symmetry, the dimension, and the connectedness or disconnectedness of the fractal object. For some selected triples of parameter values, a couple of well known fractal geometries (e.g. the Cantor set, the Sierpinski gasket, or the Swiss flag) can be gained as special cases.