Description with Maxima code
Boundaries of hyperbolic components of Mandelbrot sets are closed curves : cardioids or circles.
Douady-Hubbard-Sullivan theorem (DHS) states that unit circle can be mapped to boundary of hyperbolic component. This relation id defined by boundary equations. Here these equations, are used to draw boundaries of hyperbolic components. http://en.wikipedia.org/wiki/File:Mandelbrot_Components.svg
