I saw a video showing a render of ball bearings rocking forwards and backwards not colliding and making the rolling circles... So... Ya know... Thought I'd do it in scratch... If you watch any given blue spot it only ever moves in a straight line, never colliding with another ball, if you switch the lines off you really only see the rolling ball. Also, adjust the number of balls to you preferred complexity!
Technical stuff: Each ball travels in the magnitude of a sine wave, each ball sinewave is offset by the angle it's travelling at.