Complex Exponential Circle Fractal
Complex Exponential Circle Fractal
A circle rotates with angular velocity inside another circle . Inside , a circle rotates with angular velocity . Inside , another circle rotates with angular velocity ω, 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.
C
2
ω
C
1
C
2
C
3
αω
C
3
C
4
2
α
C
n