Douady's rabbit is the Julia set of \(p(z) \approx z^2 - 0.123 + 0.745i\text{.}\) More precisely, it's the Julia set of \(f_c(z)=z^2+c\) where \(c\approx -0.123 + 0.745i\) is chosen so that \(f^3_c(0)=0\text{.}\) As a result, \(p\) has a super-attractive orbit of period 3.

Douady's rabbit is shown in figure Figure 1 with the critical orbit shown in red.

An interactive orbit generator for this function is included on this webpage: https://goo.gl/04o9AY.