I'm going by the maxim Groups, like men, are known by their actions This naturally leads one to ask "given groups $G, H$ which act on sets $S, T$ and the semidirect product $G \rtimes H$, how does one visualize the action of $G \rtimes H$? What does it act on? Some combination of $S$ and $T...

If you do the following: Place random points on a finite surface Draw the Voronoi diagram using the points as germs Calculate the centroid of each cell Repeat step 2 and 3 indefinitely using the centroids obtained in step 3 as germs. How does that look like? Does it converge to a diagram wher...