Mathematics · Study 047
Lorenz Attractor
Two trajectories of the Lorenz system start a hair apart and trace the famous butterfly in 3D. Rotate the attractor with your pointer.
What you're looking at
Three coupled equations move a point through space. The white and red paths begin one ten thousandth of a unit apart. Both are drawn to the same two lobed shape and loop around it forever, yet after a short while they are on different lobes at any given moment.
The idea behind it
Edward Lorenz found this behaviour in 1963 while running a stripped down weather model. Rounding a starting value to three decimal places gave a completely different forecast. The result put a hard limit on long range weather prediction and gave the butterfly effect its name.
Try this
Move the pointer to rotate the view. Restart to release both paths together again.
