Chaos Lab #1c

Koenigs-Lemeray Construction for the Cubic Family

Note: State space is [-1, +1], control space is [0, 2.66]

Suggestions

When you move the slider, you:
  • adjust the control parameter [ R in the logistic function, R*X*(1-X^2) ]
  • redraw the green graph of the logistic function, X between 0 and 1, and
  • clear the screen of the red KL web
  • BUT, the current value of X is remembered.
Experiment with values of R everywhere, but especially:
  • R around 0.8: an attractive fixed point at 0
  • R around 1.5: an attractive fixed point at +0.5
  • R around 2.5: an chaotic attractor on the right side

Revised 11 Sept 2002 by Ralph Abraham