Complex Exponential Circle Fractal

ratio r between circles

0.5

ratio α between angular velocities

-2

time t

0

show fractal

A circle

C

2

rotates with angular velocity

ω

inside another circle

C

1

. Inside

C

2

, a circle

C

3

rotates with angular velocity

αω

. Inside

C

3

, another circle

C

4

rotates with angular velocity

2

α

ω

, and so on. Plotting the path of the limit of the centers of the

C

n

can give interesting-looking fractals. It is not hard to prove that these curves are self-similar.