Wolfram Demonstrations Project

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.

The curve is the plot of the complex numbers

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Complex Exponential Circle Fractal