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Complex Exponential Circle Fractal

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A circle rotates with angular velocity inside another circle . Inside , a circle rotates with angular velocity . Inside , another circle rotates with angular velocity , and so on. Plotting the path of the limit of the centers of the can give interesting-looking fractals. It is not hard to prove that these curves are self-similar.

Contributed by: Brian Burns and Emile Okada (February 2013)
Open content licensed under CC BY-NC-SA

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The curve is the plot of the complex numbers .

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