The harmonograph is a 2-dimensional system described by the following equations:
By sheer coincidence I encountered a harmonograph at Portland's Oregon Museum of Science and Industry (OMSI) a few days after reading about them on Paul Bourke's excellent website. It as fun to see a physical machine in action after reading about them. The device was an excellent way to introduce dampened harmonic motion to kids, who lined up to have the machine create images to take home.
Harmonograph
Animated harmonograph