I had the random idea this morning to consider Voronoi diagrams using the distance induced from some leaper. For the vanilla knight \(L(1,2)\), for example, pick squares on the infinite chessboard and color them uniquely. Call these the seeds. Then color each other square on the board the color of the closest seed, where distance is the fewest number of \(L(1,2)\)-moves needed to get between two squares. Here is a Voronoi diagram using \(L(1,2)\), where there are eight seeds placed around a circle of radius 200 (on a 1000x1000 board):

I'm interested in what happens when we fix the set of seeds and vary the metric. For instance, keeping the same seeds as the above picture but using an \(L(1,6)\) leaper, we get this much wavier picture:

I've used the same seed set as above, but varried the leaper along \(L(1,i)\) for \(1\leq i \leq 50\). I slowed down the first few frames of the following gif so you can see the structure before it starts to devolve:

But I think the best one so far is choosing \(L(i, i+i) \). I've changed the color palette to fit the fall time and generated the first 477 frames of this changing diagram.