A Douady rabbit is a fractal derived from the Julia set of the function f c ( z ) = z 2 + c {\textstyle f_{c}(z)=z^{2}+c} , when parameter c {\displaystyle c} is near the center of one of the period three bulbs of the Mandelbrot set for a complex quadratic map.
It is named after French mathematician Adrien Douady.