Interesting curved surfaces from ideas of Voronoi Diagram.
A Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane. That set of points is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any other. The boundaries of the Voronoi diagram is all points on the lines in the diagram, so that the points are equidistant to the nearest two (or more) source points. The interesting curved surfaces were constructed based on some forming characteristics of Voronoi Diagram.
GIFs by Daniel Piker - Space Symmetry Structure‘s blog.
In 2 dimensions a Voronoi diagram partitions the plane(2D) according to proximity to points (0D), with the boundaries being lines (1D)
In 3D we can also divide space according to proximity to points, giving polyhedral cells -like bubbles in a foam- and this is usually what is referred to as a 3D Voronoi.
Ideals: However, there is another way of generalising from 2 to 3D that is arguably more natural. Before, we had an (N)Dimensional space partitioned according to proximity of (N-2)D objects and the boundaries were (N-1)D objects.
So taking N=3, we have a division of 3D space by surfaces according to proximity to lines.
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