ABSTRACT
This chapter introduces the notion of the Julia set of a complex function. The Julia set is the place where all of the chaotic behavior of a complex function occurs. For the squaring function, the orbit of any point inside and on the unit circle is bounded; points outside the unit circle have unbounded orbits. For the squaring function, only points on the unit circle have supersersitive orbits. The chapter considers the quadratic functions Qc(z) = z2+ c in case ∣c∣ > 2. The easiest way to compute the filled Julia set is to use the definition of Kc. The chapter then discusses three examples of specific Julia sets for Qc. Each of these Julia sets exhibited certain properties: repelling periodic points were dense in the Julia set and Qc was supersensitive at any point in Jc. Both of the properties hold the Julia set of any Qc.
