FEIGENBAUM NUMBER

LOGISTIC MAP:

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

a: 0 -> 4

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

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

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