Voronoi Bubbles

Given a set of points in the plane, the Voronoi diagram partitions space into regions where each region contains every location closer to its seed point than to any other. The cells tile space perfectly, with shared edges marking the lines of equal distance between neighbors. This simple geometric idea governs an enormous range of natural structures: the cracking of dried mud, the cells of biological tissue, the territories of birds, the foam of soap bubbles, the structure of metallic grains. By choosing different point distributions — Poisson, jittered grid, centroidal relaxation — you get different organic vocabularies. Every image here is a literal Voronoi computation over carefully placed seeds, rendered with shaded cells and crisp edges.

V(p) = {x | d(x,p) ≤ d(x,q) ∀ q ∈ P}