Task

Calculate the Feigenbaum constant.



See

   Details in the Wikipedia article:   Feigenbaum constant.


maxit = 13;
maxitj = 10;
a1 = 1.0;
a2 = 0.0;
d1 = 3.2;
a = 0.0;
Table[
  a = a1 + (a1 - a2)/d1;
  Do[
   x = 0.0;
   y = 0.0;
   Do[
    y = 1.0 - 2.0 y x;
    x = a - x x;
    ,
    {k, 1, 2^i}
    ];
   a = a - x/y
   ,
   {j, maxitj}
   ];
  d = (a1 - a2)/(a - a1);
  d1 = d;
  a2 = a1;
  a1 = a;
  {i, d}
  ,
  {i, 2, maxit}
] // Grid