Feigenbaum Constants - The First Constant

The First Constant

The first Feigenbaum constant is the limiting ratio of each bifurcation interval to the next between every period doubling, of a one-parameter map

where f(x) is a function parametrized by the bifurcation parameter a.

It is given by the limit:

where an are discrete values of a at the nth period doubling.

According to (sequence A006890 in OEIS), this number to 30 decimal places is: δ = 4.669 201 609 102 990 671 853 203 821 578(...).

Read more about this topic:  Feigenbaum Constants

Famous quotes containing the words the first and/or constant:

    The first of the undecoded messages read: “Popeye sits in thunder,
    Unthought of. From that shoebox of an apartment,
    From livid curtain’s hue, a tangram emerges: a country.”
    John Ashbery (b. 1927)

    Henry David Thoreau, who never earned much of a living or sustained a relationship with any woman that wasn’t brotherly—who lived mostly under his parents’ roof ... who advocated one day’s work and six days “off” as the weekly round and was considered a bit of a fool in his hometown ... is probably the American writer who tells us best how to live comfortably with our most constant companion, ourselves.
    Edward Hoagland (b. 1932)