Saturday, August 01, 2020

[thfgbuze] Onset of chaos

Given any function f(x) of the right shape ("one hump"), the map x <- r*f(x), with r being adjusted, will manifest period-doubling bifurcations according to Feigenbaum's Constant and will have an onset of chaos at its accumulation point.  The oft-demonstrated logistic function f(x) = x*(1-x) is one of the simplest functions with the right shape, with chaos starting ar r ~= 3.5699 (OEIS A098587).  For a given function, where will its first onset of chaos be?

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