Halvorsen

Halvorsen Attractor — A chaotic system with three-fold rotational symmetry, producing a distinctive pinwheel-like shape. The attractor consists of three intertwined lobes that spiral around each other, creating a visually complex but structurally symmetric trajectory.

dx/dt = −ax − 4y − 4z − y²
dy/dt = −ay − 4z − 4x − z²
dz/dt = −az − 4x − 4y − x²

Open Halvorsen 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.