Halvorsen attractor
The Halvorsen attractor is a chaotic system with three identical wings arranged around the diagonal x = y = z.
Equations
dxdt=−ax − 4y − 4z − y2
dydt=−ay − 4z − 4x − z2
dzdt=−az − 4x − 4y − x2
The equations are cyclically symmetric. Replace x with y, y with z and z with x, and the system maps onto itself. A rotation of 120° about the diagonal does the same thing to space, so whatever the flow does in one wing it does in the other two.
History
The system is named after Arne Dehli Halvorsen.
What to look for
This page opens looking straight down the diagonal, where the three wings sit 120° apart. Turn it away from that axis and the symmetry disappears into a knot of ribbons. The app centres the view on (−2, −2, −2), a point on that diagonal.