Thomas

Thomas' Cyclically Symmetric Attractor — Introduced by René Thomas, this system has the elegant property of cyclic symmetry: each variable is damped and driven by the sine of the next variable in the cycle. The parameter b controls dissipation; as b decreases the system transitions from stable points through limit cycles to chaos.

dx/dt = −bx + sin(y)
dy/dt = −by + sin(z)
dz/dt = −bz + sin(x)

Open Thomas in chaosrack →

It opens running, on the model selector, with its own knobs. Rotate it by dragging, zoom with the wheel, and turn the parameters to see what the figure does when the system changes.