Optimization-Based Tree Modeling

Kevin Wampler

Trees are pretty, mostly
And have such a graceful form,
But are hard to model closely
with the L-systems that are the norm.

These methods make a useful hammer
So we treat botany as a nail,
But with such reliance on a grammar
Biological significance is bound to fail.

So sing to me oh Muse,
Of such things as roots and leaves,
So this situation we may unconfuse,
And find a better way to model trees.

At first this problem did seem quite tough,
But soon the riddle was unfurled,
The answer become clear enough,
If you look into the real world.

A tree's growth must fit constraints,
Must account for costs and gains,
Some times grow fast, others with restraint,
For it has a life it must maintain.

The parameter space is rather large,
We must find where the maximum lies,
But fortunately it is not so hard,
To program a computer to optimize.

So we start out with this rather simple form,
And although it does not look too real,
With some work we can make it conform,
To something with a slight bit more appeal.

To optimize it seems only right,
To do what is done by trees,
To maximize the amount of light,
that falls upon its leaves.

To model competition,
We decrease the low light that is around,
And get a species with a disposition,
To reach high above the ground.

So the project was in part success,
Thought there is much left to be done,
To model more species, physics and stress,
To have trees respond to more than just the sun.
But in the short time we tried our best,
And at the very least,
Found it all to be quite fun.