These spirographs are roulette curves obtained by rolling a circle of radius around a circle of radius .[more]
Explore orbits from two circular standing waves with large amplitudes () with the frequency sliders. Integer values (1 to 6) and reciprocals of integers (1/2 to 1/7) inputs give interesting patterns.
Crank up the cycles slider if the orbit is not closed.
See wave 1 morph into wave 2 using the morph slider (left to right).
Explore how phase shifts affect the orbits. For the integer and reciprocal of an integer inputs you can always find a symmetrical orbit, and another one with phase shift of wave 2 increased by . Or see how, with , a phase shift approaching obliterates the wave by interference.[less]