The Broken Stick in n Dimensions

number of runs to average

dimension of hypercube

number of partition points

The broken stick problem in

n

dimensions begins with a unit hypercube and divides it successively by

n

2

planes perpendicular to the axes into successively smaller rectangular parallelepipeds. At each iteration, only one of the rectangular parallelepipeds is randomly chosen to be divided. Then the resulting distribution of volumes, displayed for any number of iterations, can be seen to show a power-law distribution (graphed in log-log space).