Feigenbaum universality: period-doubling ratio (r_{n+1}-r_n)/(r_{n+2}-r_{n+1}) -> delta = 4.66920...

Feigenbaum period-doubling universality framework. Setup: for a smooth unimodal 1D map f_r(x) (e.g. logistic x -> r*x*(1-x), sine x -> r*sin(pi*x), cubic, ...) as the control parameter r is increased the attractor undergoes an infinite…