#leaf venation

Colourful venation.

I'd already set up the venation code so that it's easy to swap renderers. This one just iterates over all of the vein nodes and draws a bunch of circles, remembering the colour of each node as it goes.

This version also implements "anastomses," the places where the veins reconnect and form loops. Another update was made to get rid of live lock states when auxin hormone sources were placed on either side of a vein and it didn't know where to place the next vein node.

This will need some optimization before it can scale.

Leaf Venation Algorithm. Algorithms as art?

Anders Hoff's leaf venation work was making me jelly. Decided to have a go at the algorithm in Processing using the paper Anders recommended (below). This animation is a visualization of the algorithm in action.

The white circles are the leaf venation nodes. These will form the actual leaf veins. The pink circles are sources of the auxin hormone found in plants. New leaf vein nodes grow toward auxin sources and use them up, causing them to disappear. The grey area indicates this auxin hormone "kill distance."

The thin lines indicate nearby auxin sources that could influence a vein node's growth and the thick lines indicate the ones that do. I'm also drawing a stubby black line indicating the net influence on the vein node.

Visualizing it like this made it much easier to debug as I implemented the algorithm.

Next steps? Scale up the number of points being generated. Also need to look at getting the veins to connect in a grid. Eventually, I want to grow specific 2D shapes and combine it with paper-folding.

Runions A, Fuhrer M, Lane B, Federl P, Rolland-Lagan A-G, et al. (2005) Modeling and visualization of leaf venation. http://algorithmicbotany.org/papers/venation.sig2005.pdf

I think the single most interesting thing to me is the diversity in patterns and shapes there are across leaves? The thing that made me want to study leaf venation were the melastomes: 

(Miconia calvescens via Stephan Buchan, Flickr)

It makes them really easy to identify (which was helpful for me at the time, because I knew very little tropical botany the summer I did this project, and identifying tropical plants can be really, really hard!), but it's also really unusual, because the veins are joined up at the bases and then at the tips, and the overall structure is unique to the family. There are similar looking, like cinnamon (which tripped me up in a greenhouse once - got all excited then looked at the tag), but none quite the same.

(Cinnamomum varium via Wikipedia)

So I started asking what might this pattern be for? Is it just an artifact of development, or does it give some benefit to the plant? Do other plant groups have venation as similar among close relatives, like melastomes, or does it vary even in closely related species? Can plants change their venation in different kinds of stressful environments? 

Those are the questions I'm hoping to answer in my PhD!