Fractal Tree

click for some more variations

Fractal trees do seem very 80s, but I recently saw this nice interactive experiment (which was inspired by this), and couldn’t resist trying it out in a quick Grasshopper sketch.

It was easily generalised to 3D by using reference frames.
Just varying the positions of the endpoints of the first pair of branches produces a great range of forms.
When branches are of equal length to the trunk, with a separation angle of 2PI/3 and a twist of ArcCos(1/3) (the dihedral angle of a tetrahedron), the resulting tree is the skeleton of the Gyroid – the Wells(10,3)-a Net.

I think this would be a really fun thing  to link to some AR style 3d-tracking, so you could move a couple of fiducial markers around in space and have the model update in realtime.