Ikeda

Ikeda map (K. Ikeda, 1979) — light circulating in a nonlinear optical cavity, where each pass rotates the complex field by an amount that depends on its own intensity. That intensity-dependent rotation is the whole mechanism: the more energetic part of the beam turns further, and the attractor's hook is the result.

t = 0.4 − 6/(1 + x² + y²)
x' = 1 + u·(x·cos t − y·sin t)
y' = u·(x·sin t + y·cos t)

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.