LOGISTIC MAP:

Xn+1 = a*Xn*(1-Xn)

a: 0 -> 4

Bifurcation Diagram (Xn->oo as a function of a)

Xn

a (0 -> 4)

 

BIF. POINT ak value (ak-ak-1) (ak-ak-1)/(ak+1-ak)
a1 3.000000
a2 3.449490 0.44949
a3 3.544090 0.09460 4.75147991543339
a4 3.564407 0.020317 4.65619924201411
a5 3.568759 0.004352 4.66842830882361
a6 3.569692 0.000933 4.66452304394492
a7 3.569891 0.000199 4.68844221104788
.....
.....
The sequence tends to: 4.669201 Feigenbaum Number