<ul><li>The logistic map explores the behavior of a value x as the function f(x) = r*x(1 - x) is iteratively applied with x between 0 and 1 and r between 0 and 4.</li><li>For values of r between 0 and 3, the convergence of the iterates of the logistic map is analyzed in detail, focusing on the questions of whether the sequence converges, what it converges to, the qualitative convergence behavior, and the speed of convergence.</li><li>The convergence for r values below 1, between 1 and 2, and between 2 and 3 is described, highlighting how the behavior changes from monotonically decreasing to oscillating as r increases.</li><li>Specific cases like r = 1, 2, and 3 are discussed, showing that convergence can vary from slow to fast depending on the value of r, with r = 2 presenting quadratic convergence.</li></ul>

The simple part of the logistic map isn’t that simple

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