Dirichlet forms on the Sierpiński gasket

Dirichlet Forms on the Sierpiński Gasket

We study not necessarily self-similar Dirichlet forms on the Sierpiński gasket that can be described as limits of compatible resistance networks on the sequence of graphs approximating the gasket. We describe the compatibility conditions in detail, and we also present an alternative description, based on just 3 conductance values and the 3-dimensional space of harmonic functions. In addition, w...

Hanoi attractors and the Sierpiński gasket

The famous game Towers of Hanoi is related with a family of so–called Hanoi–graphs. We regard these non self–similar graphs as geometrical objects and obtain a sequence of fractals (HGα)α converging to the Sierpiński gasket which is one of the best studied fractals. It is shown that this convergence holds not only with respect to the Hausdorff distance, but that also Hausdorff dimension does co...

Sierpiński gasket graphs and some of their properties

Block-Space GPU Mapping for Embedded Sierpiński Gasket Fractals

This work studies the problem of GPU thread mapping for a Sierpiński gasket fractal embedded in a discrete Euclidean space of n × n. A block-space map λ : Z2E 7→ Z 2 F is proposed, from Euclidean parallel space E to embedded fractal space F, that maps in O(log 2 log 2 (n)) time and uses no more than O(n) threads with H ≈ 1.58... being the Hausdorff dimension, making it parallel space efficient....

Energy and Laplacian on the Sierpiński Gasket

This is an expository paper which includes several topics related to the Dirichlet form analysis on the Sierpiński gasket. We discuss the analog of the classical Laplacian; approximation by harmonic functions that gives a notion of a gradient; directional energies and an equipartition of energy; analysis with respect to the energy measure; harmonic coordinates; and non self-similar Dirichlet fo...