This simulation shows a self-similar k-regular fragmentation with splitting rate q. We start with the unit interval. At rate 1, the interval splits into k parts of equal size. Recursively, each interval of size x splits now into k parts of equal size at rate q^x indepedently. When q<1, i.e. the smaller the fragment get, the longer it takes on average until it branches again, consider the size of the smallest and largest size of a fragment at a given time.

In the following, we give a visualization for this procedure for general values of k and q. We always let q be in (0,1] and distiguish between the slowed down case and the explosive case (in the latter, q is replaced by 1/q). We give the total number of branches as well as the minimal and maximal number a segment has branched at a given time. Moreover, we visualize the graph, which we obtain by ploting the midpoints of the segments over time, and provide example parameters for q=1, q<1 and 1/q<1. Note that for simplicity, we assume that there is at most one branch in each time interval of length 0.01 and we stop counting after (at most) 14 branches , when this can no longer be properly depicted on a usual screen.

Enough for the description - Have fun with the simulation :)