Feigenbaum constant
There are two
mathematical constants called
Feigenbaum constants. Both express ratios in a
bifurcation diagram. is the
ratio between successive bifurcation intervals, or between the diameters of successive circles on the axis of the
Mandelbrot set. is the ratio between the width of a tine and the width of one of its two subtines (except the tine closest to the fold).
These numbers apply to a large class of dynamical systems, not just to the logistic map.
Both numbers are believed to be transcendental although they haven't been proven to be so.