Sadly the original bl.ocks.org seems to be dead. Hopefully you can still see the visualization at this clone.
Inspired by Amit Patel's diagram illustrating cube coordinates. That diagram initially confused me because the edges of the grid cubes centered on integer coordinates in the plane x + y + z = 0 don't themselves lie in the plane, so it seemed like the animation "cheated" at the end by dissolving to planar hexagons. But of course the point is just that the silhouettes of those cubes form a perfect hexagonal tiling of the plane. That tiling is highlighted as red hexagons here.
I made this animation to get a better intuition for how those cubes intersect the zero plane. It shows what happens as we slice the cubes at x + y + z = w while reducing w towards 0. Fittingly the slice where the zero plane intersects each cube is in fac