Halvorsen Attractor

Cyclically symmetric strange attractor — 3D point cloud colored by velocity

dx/dt = -ax - 4y - 4z - y² | (cyclic: x→y→z→x, Z3 symmetry)

Parameter a

1.40

Point Count

3000

Rotation Speed

0.30

Point Size

The Halvorsen attractor has cyclic symmetry x→y→z→x under Z3 (120 degree rotations). Largest Lyapunov exponent approx 0.79 — sensitive dependence confirmed. Colors encode velocity: blue=slow, cyan, white, yellow, red=fast. Drag to rotate. Attractor dimension approx 2.06 by Kaplan-Yorke formula.