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Very nice.

Is there any way to control balance? Could there be?

That's a good idea- bias in one direction or the other could create wind-swept looking trees. I'll throw that in later tonight.
Awesome. That could make for an interesting model of skew versus sun direction/latitude, too.
a randomness/mutation/imperfection slider would be neat, especially if it could cause chaos along a branch and its nodes.
Neat. Apparently, it makes root vegetables too :)

Trunk Width: 200 segment length: -30 branching angle: 100 branching symmetry: 50

Playing with the settings, different species of trees come to mind... It would be really interesting to classify and group trees by these parameters.
Just added that bias setting. Now you can make windswept trees: http://www.filosophy.org/projects/trees/#jwi3ouq0U

I like the idea of classifying trees by looking at the parameters of the branch structure -- I think that kind of approach would very well complement traditional computer vision methods.

Another thing that I've been wanting to play with is creating a 'forest' of these kinds of parametrizable trees and running a genetic algorithm to see what parameters win out in collecting "sunlight", etc. Could be fun, but would take a bit longer to make...

Very nice.

Forests could be cool...creating a genetic algorithm for such a forest could be a lot of work and lead to less interesting results than expected...