The Rabbit and Other Julia Sets Wrapped in Sierpin´ski Carpets

For these maps, the point at ∞ is always a superattracting fixed point, so we have an immediate basin of attraction of ∞ that we denote by Bλ. As a consequence, we may also define the filled Julia set for these maps to be the set of points whose orbits remain bounded. We denote this set by K(Fλ).