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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