VMI Research

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
Seen in 1963 by Ed Lorenz, Cambridge, MA In simulation of a global climate model It is the source of the "butterfly effect" concept
In simulation of a global climate model It is the source of the "butterfly effect" concept
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: 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: 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: 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: 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: visual-chaos.org They play in NetLogo 3-D, you may download it from NetLogo Home.