Abstract
We study the mathematical accuracy of computer algorithms used to produce pictures of Julia sets by analyzing two representatives cases of the complex exponential function. We first define the Julia set and give the simple algorithm used for the exponential function. We then define what it means for a picture to be "right" and consider the two totally different Julia sets of E0.3(z) = 0.3ez and E(z) = ez. We use a simple expansion argument together with the properties of the exponential function to show that each of these pictures is correct.
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