Voronoi Diagram

Voronoi diagram, which is also called Voronoi tessellation, Voronoi decomposition, or Dirichlet tessellation, is a particular type of decomposition of a metric space, which is originally developed by Dirichlet and Voronoi. Voronoi diagrams are defined as followings;

Suppose that P = {p1, p2, p3, …. , pn} is the set of points on the plane. (Such point are called a site.)

V(pi) = { q| dist(pi,q) less than dist(pj,q) , j != i }

where, V(pi) is called the Voronoi cell for pi, and is the set of q which are closer to pi than any other sites.

According to the definition of Voronoi diagrams, a Voronoi edge is the perpendicular bisector between pi and q.

On the other hand, Delaunay triangulations are the dual graph of Voronoi diagrams for the same set P as the figure above shows.

For more detailed information and explanation of Voronoi diagrams and Delaunay triangulation, see websites, for example Wikipedia.

www.en.wikipedia.org/Voronoi_diagram
www.en.wikipedia.org/wiki/Delaunay_triangulation

According to the properties of Voronoi diagrams, there are various applications in many fields. For example, in geophysics and meteorology, the diagrams are used to analyze spatially distributed data including rainfall measurement. For anthropology, explanations of area in relation to influences of different cultures. For economists, the best distribution, model market. For ……… The list of applications are endless. Above all, one of the most famous applications is Snow’s Report on the Cholera outbreak in 1854. He used a Voronoi diagram to investigate distribution of the dead and area of assumed contaminated water.

Snow's map for Cholera

Meanwhile, what is the situations of Voronoi diagrams in design field including art, architecture, etc?? Due to nature-like and aesthetic outlooks, Voronoi diagrams are used by plenty of artists and architects. In fact, it is quite easy to find works in relation to the Voronoi tessellation. Their works are quite interesting and attractive. However, we might not be able to discover the ones which is associated with not only aesthetic composition of Voronoi diagrams, but also their mathematical properties that are applied to many researches in other fields as mentioned above. It may be because art or architecture is slightly different from other fields in terms of scientific researches. However, at the circumstances, beauty of scientific basis is probably necessary at least in architectural field according to the increases of environmental problems.

Biomimetic Butterflies : flight404

Yearbook pictures: Golan Levin

If so, how can the scientific beauty of Voronoi is achieved or applied into architectural field?? It is not easy for me to describe the exact examples or answers for the question, but there may be possibilities for me to find out the way of optimized area division at arbitrary point of façade in terms of internal space and external environmental influence, which is combined with sustainable design, especially energy efficiency. The idea is still developing and unfinished, but as soon as possible it is aimed to accomplish in near future.

Grotto: Aranda Lasch

AlgorithmicSpace: 000studio