3D Percolation Cluster Accessibility

March Meeting 2010

A three-dimensional percolation cluster with sites colored according to their accessibility to diffusing random walkers


David A. Adams
Leonard M. Sander

Department of Physics
University of Michigan
Ann Arbor, Michigan

Robert M. Ziff
Department of Chemical Engineering
University of Michigan
Ann Arbor, Michigan

3D Percolation Cluster Accessibility

Fractals are self-similar, they look the same at many scales, and occur frequently in nature so they are the subject of sustained theoretical, experimental and aesthetic interest.

An important property of a fractal is how easily tiny dust particles can reach different parts of the object. This property is called the harmonic measure and is important for applications such as how a rough catalyst grows and how resilient rough catalysts are to being contaminated by non-reactive molecules. The harmonic measure is frequently difficult to obtain because the innermost parts of a fractal objects typically have probabilities smaller than one in a billion-billion of being hit by the dust particles.

We developed a tool to measure those extremely small probabilities on simulated three-dimensional fractal objects called percolation clusters. The pictures shows a small percolation cluster with the sites on the cluster colored according to their portabilities of being hit by dust particles.

Usage Information

The image was created and is owned by David A. Adams at the University of Michigan. Reporters may freely use this image as long as they include the following credit: "Image courtesy of D. A. Adams/University of Michigan".

For further information, contact:
Jason Bardi
(301) 209-3091