A Voronoi diagram is a visual representation of relative distance between several points on the plane. For a given point on the plane (in most examples and in my examples below the point is coloured black) a colour is assigned, and all surrounding pixels to that point are coloured the assigned shade if they are closer to that point than to another. So, as you get further from a point eventually a given pixel is closer to another point than to the one we were first concerned with, and that pixel is coloured the assigned colour of that other point. So a given pixel is coloured black (usually, but no one can stop you from not doing so if you like) or is coloured the assigned colour of the nearest key point.
So, one can think of the solid colour areas as the area of influence of the point that colour was assigned to that is somewhere within that solid region. That is one way to think about it, see the wikipedia entry linked above for a far better explaination that I have supplied, along with a partial list of applications of these diagrams.
A while ago a friend of mine was talking about ways to tessellate 2 dimensional images for a certain effect he wanted. He was talking to me about this and mentioned he thought interpolating a given image as a Voronoi diagram could give him the effect he wanted if consistent reference points and colour mappings were possible. I wasn’t at the time familiar with these diagrams and read up on them. The first question was if an original image could be discerned from such a diagram, and I offered to throw together a quick proof of concept program (the friend in question is far and away a better programmer than I am, but I have been doing computer imagery for a long time and I also have a formal mathematics education whereas he does not. I still am deeply in his debt for his help in many of my projects).
| Here is an example of what the first images we produced looked like. |  |