Ratios..........his 1st..........

The first constant[edit]

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

${\displaystyle x_{i+1}=f(x_{i}),}$

where f(x) is a function parameterized by the bifurcation parameter a.
It is given by the limit^[2]

${\displaystyle \delta =\lim _{n\to \infty }{\frac {a_{n-1}-a_{n-2}}{a_{n}-a_{n-1}}}=4.669\,201\,609\,\ldots ,}$

where a_n are discrete values of a at the n-th period doubling.
According to (sequence A006890 in the OEIS), this number to 30 decimal places is δ = 4.669201609102990671853203821578….

Illustration[edit]