Voronoi

I was completely fascinated with math in high school, binary numeral system was my favorite (here is a binary generated from it's digitalicious), and the process of proving theorems in geometry. I wish go back in time and stick with that subject. Or that I have the computer power to generate some of these algorithms on my computer. Ok, that was all a long time ago, but time does not lessen my love for it all.

So I came across Voronoi: In mathematics, a Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g., by a discrete set of points. It is named after Georgy Voronoi, also called a Voronoi tessellation, a Voronoi decomposition, or a Dirichlet tessellation (after Lejeune Dirichlet).



It was this post on Processing Blogs: "Voronoi" that got me going. The re-creation of the butterfly wing! Seen below. I would love to have a print ... off the investigate that.

"The outline of the butterfly wings was made procedurally with Processing (based on the wing form of the African Monarch). I placed magnetic particles all along the contour of the wing, dropped in a few gravity particles and a few hundred magnetic particles and let them settle into place. These particles are then used as the center sites for a Voronoi algorithm to create the vein-like structure that spreads through the form.

These Voronoi wings are but a sampling of the many different types of algorithms that are being explored to create a nice variety of wing forms. I will be posting more about it once the installation is complete and hope to have better documentation of the piece."



Voronoitom

Geometry Junkyard

MATSYS has a good explanation: Voronoi Morphologies, "Morphologies is the latest development in an ongoing area of research into cellular aggregate structures. The voronoi algorithm is used in a wide range of fields including satellite navigation, animal habitat mapping, and urban planning as it can easily adapt to local contingent conditions."