Buttons
- KL Step: does one step of KL process (vertigo-horrid)
- Clear: removes red cobweb, retains current value of X
- Reset: removes red cobweb, resets X to slider value X0
Sliders
- R may be changed by dragging the blue disk up and down.
When you change R, you:
- adjust the control parameter [ R in the logistic function, R*X*(1-X) ]
- redraw the yellow graph of the logistic function, X between 0 and 1,
- the red cobweb is remembered, and
- the current value of X is remembered.
- X0 may be changed by sliding the green square along the red diagonal.
When you change X0, you:
- change the value of X0 for the next KL click
- clear the red cobweb, and
- reset the value of X to X0.
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
Experiment with a few different values of X0, eg:
- 0.5
- in interval (0.0, 0.5)
- in interval (0.5, 1.0)
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