A Voronoi diagram is a way of dividing space. It is a tessellation where a surface is partitioned into regions, each consisting of the set of points closest to a specific “seed” point. Named after mathematician Georgy Voronoy, these geometric arrangements appear frequently throughout the natural world in both living and non-living systems. This prevalence is a result of underlying principles of growth, competition, and physical efficiency.
Understanding Voronoi Formation
The formation of a Voronoi diagram is governed by the “nearest neighbor” principle. For a set of distinct points, or seeds, the space is divided into cells where every location is closer to that cell’s seed than to any other. The boundaries of these cells are lines exactly equidistant between the two nearest neighboring seeds.
This partitioning is like drawing service districts for libraries in a city, where each library’s district is the area closest to it. The resulting map forms a Voronoi diagram. This process works regardless of how the seeds are arranged, as the same proximity rule defines the boundaries.
Voronoi Structures in Living Organisms
Voronoi patterns are frequently observed in the biological world. A giraffe’s coat pattern is a classic example, where dark patches are generated by melanin-secreting cells in the embryo. As pigment radiates outward from these cells, boundaries form where their influence meets, creating polygonal spots.
This pattern is not limited to mammals. The network of veins in a dragonfly’s wing provides structural support and forms a Voronoi-like tessellation. Microscopically, the arrangement of epithelial cells in many tissues reveals a similar structure as they grow and press against one another, ensuring tight, efficient packing.
Voronoi Patterns in Non-Living Nature
Voronoi patterns also manifest in non-living systems as a result of physical processes. The polygonal cracks in drying mud are a common example. As the mud contracts, tension is released through intersecting cracks that partition the surface into cells resembling a Voronoi diagram. Similar tessellations can be seen in desert salt flats and in certain geological formations.
Another example is columnar basalt, such as the columns of the Giant’s Causeway. As a thick layer of lava cools and contracts, fractures form at centers on the surface and propagate downwards, resulting in an array of polygonal columns. The froth of soap bubbles also demonstrates this geometry, as bubbles coalesce to minimize their surface area, a process that results in the polyhedral shapes of a Voronoi structure.
Why Nature Favors Voronoi Geometry
The frequent appearance of Voronoi patterns in nature stems from principles of competition, growth, and energy minimization. Many of these structures are the result of simultaneous growth from multiple starting points or seeds. The boundaries simply form where these growing regions meet, creating a Voronoi tessellation.
This geometric arrangement is also highly efficient. Processes in nature tend to follow paths of least resistance or seek states of minimal energy. This principle explains why the pattern appears in phenomena like cracking mud or cooling basalt, as it represents an optimal state for relieving stress.
The pattern also arises from competition for space or resources. When plants grow close together, their root systems partition the available soil and light in a Voronoi-like manner. This drive for efficiency, combined with the mechanics of growth and competition, makes the Voronoi diagram a recurring outcome in natural systems.