Interunion-wheel
UniThread Chromatics: When each thread circle is color coded with hue, the interunion turns out to be the color blending operation at the eye (incidence between the threads). Here I demonstrate the quadratic form of a ⋇ b, where the result is an epicycloid for temporal interunion and a hypocycloid for spatial interunion. Note that when a < b, the temporal interunion produces a special kind of epicycloid called "peritrochoid". For higher order forms, see the applet Interunion-Euclidean.
Spirograph: The toy spirograph has similar structures, epitrochoid and hypotrochoid, corresponding to the epicycloid and hypocycloid in this applet.
See Nathan Friend's applet for interactive spirographs.
Cyclocycloid: epicycloid, hypocycloid, epitrochoid and hypotrochoid are in general called cyclocycloid.
Epicycles & Fourier series: The higher order of cyclocycloid is a curve traced by the epicycles. When the number of epicycles is unlimited, it becomes a Fourier series.