Curiosities · Foundation · 5 min
The logistic map
One simple recurrence can settle, oscillate, or become strikingly irregular.
WHAT HAPPENS IF…Compare r=2.8 with r=3.4. Does the orbit approach one point?
Preparing your experiment…
Starting with x₀, move vertically to the parabola y=r x(1−x), then horizontally to y=x to turn the output into the next input. The fixed points solve x=r x(1−x): x=0 and, when r≠0, x=1−1/r. The latter has derivative 2−r, so it is attracting when 1<r<3.
A detail that matters
A complicated-looking finite orbit does not by itself establish chaos. The displayed model uses floating-point arithmetic.
Keep the connection going
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