Answer Happy

Computation of the Feigenbaum delta Compute the Feigenbaum delta from the logistic map. The logistic map is given by X₁+1 = μx²(1-x) and the Feigenbaum delta is defined as m-1-m-2 8 = lim 8,, where 8, = 11-00 m-m-1 and where m, is the value of μ for which x= 1/2 is in the orbit of the period-N cycle with N = 2"¹ Here is a resonable outline: Loop 1 Start at period-2" with n=2, and increment with each iteration Compute initial guess for m, using m-1 m₂-2 and 8-1- Loop 2 Iterate Newton's method, either a fixed number of times or until convergence Initialize logistic map Loop 3 Iterate the logistic map 2" times Compute x and x Loop 3 (end) One step of Newton's method Loop 2 (end) Save m, and compute 8, Loop 1 (end) Grading will be done on the converged values of , up to n = 11. Set 8₁ = 5.