It reminds me of the old LOGO turtle I used to play with when I was a kid.

why?

Because people used Spirograph to make similar patterns. And the cog wheels of her device are reminiscent of the cogs used to make Spirograph patterns also.

Spirograph is an excellent way to introduce kids to the idea of relatively prime pairs.

Because the most awesome Spirograph patterns come from the relatively prime pairs of gears.