Enter two numbers (odd or prime numbers work best) then see what spirals they make. Try 43 and 37 for starters. The moon orbits the earth, which orbits the sun. If the moon left an inky trail behind it, what would it look like?
The idea came from an art&crafts toy called Super Spirals: http://www.amazon.co.uk/Super-Spirals-1003928-Galt-Toys/dp/B007T6IKQO It still needs a bit of work to exactly replicate the toy.