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Section3.7A cubic with two attractive orbits

Consider the cubic polynomial

\begin{equation*} p(z) = -z^3 + (2.41154 -0.133695 i) z^2-(0.090706 -0.27145 i), \end{equation*}

whose filled Julia set is shown in figure Figure 1. This polynomial has attractive orbits of periods both two and three. A major point here is that more complicated behavior can arise, when the degree of the polynomial increases or, more generally, as the function becomes more complicated.

Figure3.7.1A cubic with two attractive orbits

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