Fill an infinitely long rectangular prism with a uniform distribution of points. Compute the Voronoi partition of the points. Create an animation of the cross section traveling along the long axis of the prism: polygons constantly shift in size, appearing and disappearing.

What other interesting things can we add to the animation?

Dots move along line segments representing the Delaunay graph connecting the points. Connect the dots within a cell to form a polygon whose size shrinks to zero when a internal point intersects the cross sectioning plane.

Spheres centered at internal points intersecting cell vertices.

Inscribed a sphere into each cell. Maybe Apollonian spheres.

Dissection of each cell into pyramids with apex at the internal point, and each cell face a pyramid base.

How should colors of each cell be chosen to avoid adjacent cells of the same color? I suspect no finite number of colors is guaranteed to suffice.

How can we avoid having to place all the infinite number of points before calculating the Voronoi partition?

Inspired by cross sections of foams.

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