Fractals & Chaos Lesson Recap for 1/7

We spent some time reviewing the results from Complex Paint Worksheet 2. We have observed a few things, the most obvious of which are that all Julia Sets have 180-degree rotational symmetry and the only Julia Sets that have x- and y-axis symmetry have a parameter that is a real number. It turns out that both of these observations are provable facts about Julia Sets, which we will investigate tomorrow!

Secondly, we observed that many Julia Sets are connected (areas and strings) but many are not connected. This distinction – between connected and unconnected Julia sets – will form the basis for the formation of the Mandelbrot Set. Be sure you are in class tomorrow, as it will be an important day!

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