Double cover in X Y plane:

Triple Cover in X Y plane:

A torus is outlined by a quasiperiodic flow on it. This flow is on the ''image'' torus. The flow is lifted to double and triple covers using a rotational symmetry axis as outlined in Phys. Rev. E63, 016206 (2001). The lifted flow outlines a strange geometrical structure that we playfully call a 'donut' or a 'trinut'. The geometrical structure changes as the rotation axis ''slices'' through the original quasiperiodic flow on the image torus. The simulations show how the covering flow changes as the rotation axis moves from outside to inside the image torus.

-Animation by Timothy Jones

All material and animations, unless otherwise identified, Copyleft© 2007,

The Nonlinear Dynamics Group at Drexel University.

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