Measuring shape with topology
Abstract
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 selfavoiding random walks.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 July 2012
 DOI:
 10.1063/1.4737391
 Bibcode:
 2012JMP....53g3516M
 Keywords:

 Brownian motion;
 fractals;
 geometry;
 random processes;
 topology;
 02.40.Pc;
 05.40.a;
 05.40.Jc;
 05.45.Df;
 02.40.k;
 General topology;
 Fluctuation phenomena random processes noise and Brownian motion;
 Brownian motion;
 Fractals;
 Geometry differential geometry and topology