Cobweb Diagram of the Logistic Map

The logistic map, a popular example of a period-doubling cascade developing to chaos, obeys the recurrence . The red cobweb diagram traces out the orbit of for a given value of the parameter . The orbit is chaotic when the cobweb diagram becomes dense.
Use the "" slider to see periodic or chaotic orbits or one with a fixed point as the limit.
Use the "" slider to change the starting value. For a suitably high number of dropped iteration, the starting value should have a negligible affect on the plot, except in the chaotic regime.
Use the "number of iterations" slider to set the maximum chosen for plotting .
Use the "number of dropped iterations" slider to set the number of the initial iterations that are not included in the plot. If , no iterations are dropped.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Snapshot 1: period 2 orbit
Snapshot 2: period 4 orbit
Snapshot 3: chaotic orbit
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