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Last edited 22 Jul 2024

Voronoi diagram

A Voronoi pattern or tessellation is a way to divide a flat surface into different regions, where each region is a different shape and borders its closest neighbours. Each region, called a Voronoi cell, has a central point called a seed or generator, which contains all points nearest that seed. The pattern is an a efficient way to divide a two-dimensional plane and as such variations of it can often be seen in nature.

The terms originates from the Voronoi diagram in mathematics, named after the mathematician Georgy Feodosevich Voronyi who was born in 1868 in part of the Russian Empire that is in Varva Raion, Chernihiv Oblast, today Ukraine. He studied in St Petersberg in 1894 and in 1897 he defended his theses; 'On algebraic integers depending on the roots of an equation of third degree' and 'On a generalisation of a continuous fraction'. He died at the young age of 40 after a severe gall bladder attack.

Voronoi diagrams continue to be used in a variety of fields, primarily meteorology and hydrology for the weighting of precipitation data from a set of stations over an area (called a water shed). In biology they are used to study cell growth, and in ecology to study the growth of forests and their canopies, and in healthcare looking at muscle tissues.

Voronoi diagrams can also be found in computer science and informatics for example looking at the spread of networks, or material science and the formation of polymers and crystalline structure. Such models have also been employed in urban planning for zoning, in aviation for distance charts, graphic visualisation and in architecture for facade treatments and spatial planning or zoning within buildings.

Some examples of buildings expressing Voronoi tessellations are: The Home of the Arts (HOTA), opened as the Keith Hunt Community Entertainment and Arts Centre in 1986 now the Arts Centre Gold Coast (TAC) located in Surfers Paradise, City of Gold Coast, Queensland, Australia. The Spine, located in Liverpool UK has a pattern using a Grasshopper plug-in for Rhino, describing a Voronoi designed specifically to reflect the level of solar protection required over each orientation.

(image credits: MarketingHOTA, licensed under the Creative Commons Attribution-Share Alike 4.0 and AT Journal 149 Spring 'All about The Spine*, Liam Briggs MCIAT AHR.)