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... where f(a) and f(b) have alternate signs), a bracketing method, like Bisection, can be specified. The default is Bisection, for most floating point number types, employed in a manner exploiting floating point storage conventions. For other number types (e.g. BigFloat), an algorithm of Alefeld, Potra, and Shi is used by default. These default methods are guaranteed to converge. Other bracketing methods are available.
Here we test the Logistic Map using finite and infinite precision...
Here we test the Logistic Map using finite and infinite precision floats (Apfloats). More decimals produce longer sequence (longer chaotic signal for certain parameters). Shorter decimal precision makes the sequence converge to zero eventually. In the process, number of decimals rises and then drops for some reason, forming a bell-shaped curve with long tail. On second consideration, this does not look like a bell-shaped curve at all. Logistic map calculated with parameters x initial = 0.9...
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