The fractal dimension of the minimum path in two- and three-dimensional percolation

Abstract

The authors calculate the fractal dimension d(min) of the shortest path l between two points on a percolation cluster, where l approximately r^d(min) and r is the Pythagorean distance between the points. They find d(min)=1.130+or-0.002 for d=2 and 1.34+or-0.01 for d=3.