Recurrence Relation

This web page is aimed at demonstrating the recurrence relation x_n+1 = r*x_n*(1-x_n1).

You can specify the initial value of x (avoid 0), and the parameter r (1..4) and see what happens when the relation is run.

The values of x are plotted at each iteration n, and the final values, ie the values that x stabilises at, are shown. Note x will typically sequence between a series of final values.

You can also plot a so called cobweb plot of the data.

The Sweep r button automatically changes r from 2.5 and recalculates. Sweep x0 automatically changes x0 for the given r and recalculates - see the effect of initial conditions.

The Logistic Map shows the final values of xn as r is changed.

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