Deterministic Chaos

Mathematical Definition of Chaos

Dense periodic points: recall points of an n-cycle for T(x) are fixed points for Tn(x).
Also, recall the fixed points of any function are the points of intersection of the graph of the function with the diagonal line.
The animation illustrates the fixed points of Tn(x) for n = 1, 2, 3, 4, 5. Note how the fixed points fill the interval more fully as n increases.
Click the picture to animate.

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