Fractals/Iterations in the complex plane/julia/interior

" Stable orbits of polynomials may : converge to a (super)-attracting fixed point, (coverge) to a parabolic fixed point (where the multiplier is a root of unity), belong to a rotation domain (a simply connected domain on which the dynamics is conjugate to a rotation)." Lasse Rempe-Gillen mathoverflow : attractive-basins-and-loops-in-julia-sets thumb|right|DistanceToFixed Local discrete complex dynamics thumbnail|right|Types of dynamics attracting : hyperbolic dynamics superattracting : the very fast ( = exponential) convergence to periodic cycle ( fixed point ) parabolic component = slow ( lazy ) dynamics = slow ( exponential slowdown) convergence to parabolic fixed point ( periodic cycle) Siegel disc component = rotation around fixed point and never reach the fixed point When Julia set is disconnected ther is no interior of Julia set ( critical fixed point is repelling ( or attracting to infinity) References