Abstract

SummaryFunctions from the complex plane to itself are difficult to visualize; we consider the real and imaginary projections. In this paper, we explore the connections between the graphs of the real and imaginary parts of various complex functions and their corresponding filled Julia sets. We begin by examining the family of complex quadratic functions.We then expand our results to a broader collection of rational maps, including functions whose Julia sets form a Cantor set of simple closed curves, checkerboards, and a perturbed rat.

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