Algorithm for Feigenbaum's Constant
4.6692.... is Feigenbaum's Constant. Any clue as to how to generate it?
Code:
If you look at it graphically you get:
Bifurc no. Divides at Length This length/next length
------------------------------------------------------------
1 0.75 L1=1.0 L1/L2=2.0
2 1.25 L2=0.5 L2/L3=4.25
3 1.3677 L3=0.1147 L3/L4=4.492
4 1.3939 L4=0.0262 L4/L5=4.6208
5 1.39957 L5=0.00567 L5/L6=4.536
------------------------------------------------------------
Analytically it's:
Code:
Lim N L(n)
F = n -> inf ------- = 4.669...
L(n+1)
I can't even fake it numerically. No Clue.
:eek:
