Chaos Lab #1b

KL Steps for the Logistic Family, with 2 trajectories

This is a more primitive (rev 1) Tclet. Two nearby initial points are provided (not adjustable). Watch to see if they converge or diverge, for varous choices of R.

Buttons

  • KL Step: does one step of KL process (vertigo-horrid)
  • Clear: removes red cobweb, retains current value of X

Slider

  • When you move the R slider, you:
    • adjust the control parameter [ R in the logistic function, R*X*(1-X) ]
    • 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.

Suggestions

Experiment with values of R everywhere, but especially:
  • R in [0.5, 2.8]: an attractive fixed point
  • R around 3.2: an attractive 2-periodic cycle
  • R around 3.5: an attractive 4-periodic cycle
  • R in [3.6, 4.0]: lots of chaotic behavior
  • R around 3.83: an attractive 3-periodic cycle

Revised 11 September 2002 by Ralph Abraham