yAtlas

Studio · From Flow

The butterfly effect

Two starts 10⁻⁶ apart: how long until they have nothing in common?

Composing the first frame…

The gold and ice-blue orbits leave from almost the same point and at first lie on top of each other. The corner plots the distance between them on a log scale: on the attractor it grows roughly exponentially, the curve climbing in wobbles until the distance is as large as the attractor and grows no further. The moment it first passes 10 is marked t*. Each time the starting gap shrinks tenfold, t* moves back by only two or three units on average. Bring the Rayleigh number down to 20 and the strange attractor is gone: both orbits spiral in on the same fixed point, and the distance between them shrinks.