This generalization of the geometric Lorenz attractor has a curious property: every knot or (finite) link in 3-d appears as a (set of) periodic orbit(s) on this branched surface. This is a remarkable fact, in that these (infinitely many!) periodic orbits are all disjoint on the attractor. This is highly nonintuitive.
(For a proof, see the ph.d. thesis of prof/g from 1995...)
