Deterministic Chaos

6.N. Period-Doubling Scaling and the Feigenbaum Constant

The Feigenbaum Alpha Constant

There is another quantitative feature common to these period-doubling bifurcation sequences:

Here we see the distances a1 and a2 for superstable 2-cycle and superstable 4-cycle.

The next picture shows the relative placements of a1, a2, a3, and a4 in the bifurcation diagram, with the horizontal scale suitably expanded to make these distances visible.

More numerical experiments indicate the sequence of ratios an/an+1 approaches a limit, the Feigenbaum alpha constant 2.502907876... .

Return to the Feigenbaum Constant.