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The physics of a tree blowing in the wind is very difficult to model because the system is highly nonlinear. I made a numerical model of the system by expressing it as a fractal.

Max wind speed: 0.50
Wavelength (time steps per cycle): 350
Rotational k: .05

Fractal Tree

Use the sliders to change the model's parameters and look for different types of resonance. You'll find that the tree quickly stops acting like a tree but does show several interesting types of chaotic and periodic motion.

I made an ipython notebook to analyze the motion of this tree more rigorously for my applied math course. We also made a poster.

Each circle represents a base unit of a fractal. The lines connecting these circles have restoring forces both in the angular and lengthwise directions. For each time step, the fractal uses a recursive tick() function to update physics at every node and a recursive draw() function to re-render the fractal. The wind's force is given by a force object.