%0 Journal Article
%T Measuring Shape with Topology
%A Robert MacPherson
%A Benjamin Schweinhart
%J Mathematics
%D 2010
%I arXiv
%X We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We demonstrate the utility and computability of this measure by applying it to branched polymers, Brownian trees, and self-avoiding random walks.
%U http://arxiv.org/abs/1011.2258v2