These animations have been built using the relaxation algorithm.
A 300 frame animation with no drag based on the dual of the second iteration spoked triangle.
A 100 frame animation with the same starting configuration as before, but with drag included. where the
pervious version bounced around all over the show, this one settles on a fairly stable configuration,
though if you run if for a few thousand more iterations it will undergo the "Spontaneous Symmetry Breaking"
described on the Relaxation page.
version
The square version of the previous 100 frame damped triangle animation.
Our relaxation model assumes that in the relaxed state all the springs should be the same length.
The dodecagon on the left is relatively stable because the symmetry means that the forces at each
point balance out. If you run a relaxation calculation on it, the small errors introduced by using
finite precission floating point maths means that it will eventually collapse, but in the animation
here we've spead up this process by giving a small kick to one of the edge points.
There is a second version of this animation, with damping applied here.
