The Lorenz Attractor

  • The second chaotic attractor to be discovered
  • Seen in 1963 by Ed Lorenz, Cambridge, MA
  • In simulation of a global climate model
  • It is the source of the "butterfly effect" concept

  • We show four movies:
  • Movie #0: Orientation in 3D
    The view point gazes at the origin and rotates in the ZX plane
  • Movie #1: Fractal geometry of the attractor, R=28
    A trajector (green sphere) leaves colored drops on the attractor
  • Movie #2: Sensitive dependence an initial conditions, R=28
    Two trajectors (green, blue) diverge from very close initial conditions
  • Movie #3: The bifurcation sequence
    Attractors for several values of R are superimposed:
    R=0.5, 7, 14.5, 20, 22.4, 24.5, 28

  • Revised 28 July 2005 by Ralph Abraham

    PS: on 06 February 2006: this page was for a show at SigGraph 2005 and the movies may now be found at: They play in NetLogo 3-D, you may download it from NetLogo Home.