Leaf Venation/ Hyphae Growth and Voronoi Diagrams

Today I coded a script in rhpython to perform leaf venation and made a cool discovery.

Growth of multiple colonies or veins from different starting locations will approximate the voronoi diagram for those same starting points.

Here, the hyphae start points are shown in yellow, the hyphae themselves are red, and the voronoi diagram for the yellow points is shown in white. Food, not shown, is interspersed randomly throughout the surface.

This is not a REAL discovery, per se, as both patterns occur in nature as the result of similar processes (i.e. chemical diffusion). But, its still cool to see it all work out like it should.

cool stuff.

Also, if anyone knows how to turn this type of vein structure (a bunch of un-joinable lines) into a mesh surface (i.e. 3D printable), I would really appreciate that info - thanks! I have already tried messing around with topologizer and exoskeleton, to no avail.

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Replies to This Discussion

Permalink Reply by Chao Wei on November 11, 2014 at 11:29am

http://algorithmicbotany.org/papers/venation.sig2005.pdf

Permalink Reply by taz on November 11, 2014 at 2:00pm

There's a lot on the forum for creating closed 3D printable volumes from topological networks. Have you seen the original exoskeleton blog post from Daniel Piker?

http://www.grasshopper3d.com/profiles/blogs/introducing-exoskeleton...

Permalink Reply by dbffggf on September 19, 2015 at 3:22am

Hello Harrison,

I'm super interested about your hyphae growth.
Can you explain us the process? How did you do the hyphae?

Many thanks,
Great project!

Permalink Reply by Vicente Soler on September 19, 2015 at 3:51am

A voronoi cell represents the area that is closer to a particular point of a set of points. It's not surprising that any algorithm that is based on finding the closest point (nearest neighbor) will create something looking like a voronoi diagram, given enough samples to fill in the regions.

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