The complement of is the Julia set of . If all the critical points are preperiodic, that is they are not periodic but eventually land on a periodic cycle, then is all the sphere. Otherwise, is a nowhere dense set (it is without interior points) and an uncountable set (of the same cardinality as the real numbers). Like , is left invariant by , and on this set the iteration is repelling, meaning that for all w in a neighbourhood of z (within ). This means that behaves chaotically on the Julia set. Although there are points in the Julia set whose sequence of iterations is finite, there are only a countable number of such points (and they make up an infinitesimal part of the Julia set). The sequences generated by points outside this set behave chaotically, a phenomenon called deterministic chaos.
the complement of is the julia set of  if all the critical points are preperiodic that is they are not periodic but eventually land on a periodic cycle then is all the sphere otherwise is a nowhere dense set (it is without interior points) and an uncountable set (of the same cardinality as the real numbers) like  is left invariant by  and on this set the iteration is repelling meaning that for all w in a neighbourhood of z (within ) this means that behaves chaotically on the julia set although there are points in the julia set whose sequence of iterations is finite there are only a countable number of such points (and they make up an infinitesimal part of the julia set) the sequences generated by points outside this set behave chaotically a phenomenon called deterministic chaos