Wheels on wheels on wheels

by Yi Zhang

Just found this post from Walking Randomly which presents a Mathematica demo of motion path of a point of wheels on wheels on wheels:
"Wheels on Wheels on Wheels" from the Wolfram Demonstrations Project
Generally, for a series of radii r_n and corresponding spherical frequencies \omega_n, a particle on the “outer-most” wheels follows the path

z=\sum_n{r_ne^{i\omega_n t}}

I compiled another one following the demo code above, and in this one animation is among the output, besides, by inputing lists, the depth of circles is arbitrary, following pictures contains a sample with four wheels.