A cyclic 3D strange attractor with three-fold symmetry
The Halvorsen attractor is defined by:
dx/dt = -a*x - 4*y - 4*z - y^2
dy/dt = -a*y - 4*z - 4*x - z^2
dz/dt = -a*z - 4*x - 4*y - x^2
The cyclic symmetry of the equations produces a three-fold symmetric strange attractor.
At a = 1.89 the system exhibits chaotic behaviour. Nearby trajectories diverge exponentially —
the hallmark of deterministic chaos and sensitivity to initial conditions.