Here we demo a very simple maximum gap heuristic for tree cutting. Please click in the gray canvas area to add 3 or more points and see how things work. Basically, we are selecting the maximum branching height (the largest distance between two particular clusters in our dendrogram) and then splitting (or cutting the dendrogram) at half this height value. Better approaches would consider the density of all the heights present in the tree (see histogram) and select a split around the local minimum. Additionally we could take the branching density into account and cut the tree at a point just above where lots of branchings are taking place (e.g. see the plot with num of clusters (y) when cutting at height (x).