I also love using Voronoi diagrams as well as Delaunay diagrams (via Mathematica).

My most recent exploration with them was to understand and visualize the different structures and characteristics of various low discrepancy quasirandom point distributions in two dimensions.

http://extremelearning.com.au/unreasonable-effectiveness-of-...

Also interesting to compare them with @burfog's comment about the Voronoi / Delaunay diagrams of Penrose Tilings.