Fractals & Chaos Assignment for 5/22

We discussed in class that a fractional value of T will (eventually) result in a number of spokes equal to the denominator of T. If T = 1/3, for example, then every third iteration ends up exactly where you started, only closer (if you’re attracting with a value of R<1) or farther (if R > 1). But this spoke-like behavior doesn’t always appear immediately; sometimes you’ll see spirals before you see spokes. Our next question is to explore why, but first, please finish the front of the Complex Paint Worksheet. For each of these, start with R of .9, then gradually slow it down (R = .95, R = .99, R = .995, etc) so you can watch the different spiral/spoke patterns emerge. The last two can be entered as PI and PHI directly into Complex Paint.

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