Divide and conquer is an algorithm commonly used in computer science. The algorithm works on simple principle: divide the problem until a base case is found and then solve from bottom up.
If we coloured the region for points on the left purple and points on the right yellow, the boundary makes the bisector of the two halves.
Only one such bisector exists as multiple bisectors would result in the following which contradicts the division:
Credits to @shspage_en for the Voronoi script for Illustrator CC
References:
- Algorithmische Geometrie: Grundlagen, Methoden, Anwendungen by Rolf Klein
- Computational Geometry Facultat d’Inform`atica de Barcelona Universitat Polit`ecnica de Catalunya by Vera Sacrist´an
