Rössler attractor
The Rössler attractor is a single chaotic band. A point spirals outward near a plane, is lifted, folds over and drops back into the middle of the spiral.
Equations
Only one term is nonlinear: zx in the third equation. The first two equations alone describe a spiral in the xy plane that slowly grows, set by a. The z equation stays near zero until x passes c, then the zx term takes off and throws the point up and back toward the centre.
History
Otto Rössler published the system in 1976, in An Equation for Continuous Chaos in Physics Letters A. He was looking for a chaotic system simpler than Lorenz's, one whose mechanism could be seen directly: stretch in the spiral, fold in the lift, and reinject into the middle.
What to look for
Most of the time the point circles slowly near the plane. Every so often it climbs the fin, folds over and falls back in near the centre. Look from above for the spiral and from the side for the fin.