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Cobweb Diagram of the Logistic Map

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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.

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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.

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Contributed by: Kevin Reiss (May 2021)
Open content licensed under CC BY-NC-SA

Snapshots

Details

Snapshot 1: period 2 orbit

Snapshot 2: period 4 orbit

Snapshot 3: chaotic orbit

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