Why not square, triangle or circle?
In: 4542
Voronoi Relaxation / Lloyd’s algorithm (keyword to search on YouTube).
Explanation:
Imagine you are a bee and you are making a cell by putting wax around you. An other bee on the other side of the wall is also doing the same, and you are kind of pushing against both sides of the wall at the same time. The wall is made of wax and is malleable so you can squish it to make your cell bigger.
What happens if you are in a smaller cell than your neighbor? You can push against the walls around you more easily, and you have more strength than the opposite bee. So it naturally make the cell the same size.
But it also have an other effect, if you push in a corner, two bee push against you, so it pushes you away from that corner. In general, if you look at the bees when they are in the cells, they are in the center of those cells and pushing against all the walls in such a way that the area in each cell is the same as the neighboring cells. Cells with a tiny wall between them don’t push each other much, and will get closer to each other, increasing the common wall size. So it pushes all cells to have all walls the same size.
It turns out if you simulate this, you get a pretty interesting result: in a rectangle, the cells in the corner will become square, the cells in an edge will become pentagons and the cells in the middle will become hexagons. All will have the same area and because most of the cells are not in a corner or an edge, they are almost all hexagons.
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