Douady rabbit

The Douady rabbit is any of various particular filled Julia sets associated with the parameter near the center period 3 buds of Mandelbrot set for complex quadratic map. The rabbit is a parabolic Julia set for internal angle 1/3 (parameter c is a root point between period 1 and period 3 components of Mandelbrot set).

Douady's rabbit or Douady rabbit is named for the French mathematician Adrien Douady.

Fat rabbit or chubby rabbit has c at the root of 1/3-limb of the Mandelbrot set. It has a parabolic fixed point with 3 .

There are two common forms for the complex quadratic map ${\displaystyle {\mathcal {M}}}$. The first, also called the complex logistic map, is written as

where ${\displaystyle z}$ is a complex variable and ${\displaystyle \gamma }$ is a complex parameter. The second common form is

...
Wikipedia