# Voronoi Patterns

## Voronoi Diagrams

Voronoi patterns create a geometric partitioning based on the idea that regions can be created based on dividing a space closest point

> In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane. That set of points (called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any other. These regions are called Voronoi cells. The Voronoi diagram of a set of points is dual to its Delaunay triangulation.[ Wikipedia](https://en.wikipedia.org/wiki/Voronoi_diagram)

## Dragonfly Wings show Voronoi Patterning

Many natural forms display voronoi partitioning due to the growth morphologies that correspond to the growth cycles in many systems such as crystal growth, biologic cell growth, and social networks due to common dynamic physics processes. Many structural growth processes behave, according to a simple radial transformation...the system consists of a dispersed series of seed points, each point grows radially outward until it starts to interact with neighboring cells. At the point of cellular growth when neighboring cells interact, they form a boundry. In 2D space, that forms a bisection line which partitions the planar surface.

![](https://3659607454-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M0-KLg_ficxV7B_8SgA%2F-M0-KNNPhCRj2ku0AG0P%2F-M0-KRESfNXpo4Fs8a48%2FdragonflySmall.png?generation=1581627360434573\&alt=media) ![](https://3659607454-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M0-KLg_ficxV7B_8SgA%2F-M0-KNNPhCRj2ku0AG0P%2F-M0-KREUsAUZSXCoDfoO%2FsmallWing.png?generation=1581627358645240\&alt=media)

## Wikipedia Definition

> In the simplest case, we are given a finite set of points {p1, …, pn} in the Euclidean plane. In this case each site pk is simply a point, and its corresponding Voronoi cell Rk consists of every point in the Euclidean plane whose distance to pk is less than or equal to its distance to any other pk. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The line segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.

## D3 Voronoi Tesselation Visualization

[Iteractive Visualization - Link](https://bl.ocks.org/mbostock/raw/4060366/) ![](https://3659607454-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M0-KLg_ficxV7B_8SgA%2F-M0-KNNPhCRj2ku0AG0P%2F-M0-KRVGQmCGEvLaUs2U%2FScreenshot%202017-09-30%2021.14.19.png?generation=1581627362198477\&alt=media)

## Grasshopper

Grasshopper has several components which create Voronoi patterns. For this project, I've explored using the Grasshopper 2D and 3D Voronoi components to create objects inspired by the structure of dragonfly wings.

{% embed url="<https://en.wikipedia.org/wiki/Voronoi_diagram#:~:text=In%20mathematics%2C%20a%20Voronoi%20diagram,%2C%20sites%2C%20or%20generators).&text=Voronoi%20cells%20are%20also%20known%20as%20Thiessen%20polygons>." %}


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