# Mathematical beauty

The Voronoi design is based on a highly interesting mathematical method. It was already used by René Descartes in 1644. However, it is named after the mathematician Georgi Feodosjewitsch Voronoi. He used the method in 1908 in his studies in three and more dimensions. The Voronoi diagram is a decomposition of space into specific regions.
One starts with a given number of points. These points are distributed arbitrarily over a surface. They form the so-called centers. Around each centre a circle begins to grow, each at the same speed. At some point the growing circle lines meet and therefore have no possibility to expand in the usual round form - they continue to grow along the intersection lines. The resulting different sized fields within the pattern are called Voronoi regions. The borders of the regions between two points then have exactly the same distance to these neighbouring points.

The method simulates a very natural, uniform growth and is therefore an important model for illustration in many areas. For example, it can be used to simulate forest growth or even urban growth. Somewhat more complex applications can be found in image processing in the field of astrophysics.

Thus it becomes clear that the obvious natural beauty is always based on mathematical principles.

- Dr. Daniel Sommerfeld, mathematician and PIM manager in the ACO Group

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