These regions are called Voronoi cells. The Voronoi diagram of a set of points is dual to its Delaunay triangulation. Put simply, it's a diagram created by taking pairs of points that are close together and drawing a line that is equidistant between them and perpendicular to the line connecting them. That is, all points on the lines in the diagram are equidistant to the nearest two (or more) source points.

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It is named after Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi diagrams have practical and theoretical applications to many fields, mainly in science, technology, and visual art.

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In a Voronoi pattern, every point within a given region is closer to the “seed” inside that region than it is to any other point outside that region.   Each point along a region’s edge is equidistant from the two nearest seeds. It’s seen in places ranging from cracked mud to giraffe skin to foamy bubbles. Voronoi patterns can help solve geometric problems like packing, strategic placements and patterns of growth.