The evolution of the astroid pattern on the spirograph


Here is a MetaPost generated picture of the first 14% or so movements of an inner circle one quarter of the size of the outer circle (as might be found on a spirograph). This eventually generates the astroid pattern. The red arrows follow the movement of a fixed point on the smaller circle – as you can see it moves clockwise while the smaller circle moves anticlockwise relative to the centre of the larger circle.

Evolution of a spirograph pattern