bifurcation diagram of logistic map

Computational Inputs:

» parameter r:
» initial condition x_0:

Input

logistic map

Logistic map

x_n+1 = r x_n (1 - x_n) (n = (0, 1, 2, ...))

Iterates

n | 0 | 1 | 2 | 3 | 4 x_n | 0.10000 | 0.36000 | 0.92160 | 0.28901 | 0.82194

Iterates

Closed form solution

x_n = sin^2(2^(n - 1) cos^(-1)(1 - 2 x_0))≈sin^2(0.321751 2^n)
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