Faced with the problem of how to divide space, the natural world often provides the most efficient solutions. Animals from bees to fish have settled on a method that uses all possible space without leaving gaps or overlaps. The hexagonal honeycomb is a perfect example.

Mathematicians call this the tiling problem, or a tessellation. At the turn of the 20th century, the Ukrainian mathematician Georgy F. Voronoi (also spelled Voronoy) first described a mathematical tessellation in which all points in a given space are described by their nearest neighbors.

Besides inspiring artists such as M.C. Escher, Voronoi’s diagrams proved useful for defining all kinds of spaces. Some kinds of fish build their nests in groups that can be defined by a Voronoi diagram. And in the physical world, the diagrams describe basaltic lava formations and the behavior of metals.

“Voronoi diagrams provide the most uniform meshing of a sphere that we know of, and they have this remarkable property of being able to change in resolution and still be incredibly smooth,” says Todd Ringler, inventor of MPAS climate modeling (for Model for Prediction Across Scales). For climate modeling, the mathematical smoothness of the variable resolution Voronoi diagram means portions of the calculations can be broken down efficiently on a supercomputer and communications between the cells can be defined for parallel computing.

In practical terms, Voronoi tessellations are perfectly suited to the requirements of climate modeling, but for Ringler, “the only word that adequately describes them is beautiful.”