WOLFRAM|DEMONSTRATIONS PROJECT

Asymmetric Spirographs

​
radius of the circle
1
amplitude of the waves
6
frequency
f
1
of wave 1
0.5
frequency
f
2
of wave 2
0.52
cycles
12
morph wave 1  2
50
phase shifts
wave 1
0
wave 2
0
These spirographs are roulette curves obtained by rolling a circle of radius
a
around a circle of radius
r
.
Explore orbits from two circular standing waves with large amplitudes (
a=6r
) 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
180°
. Or see how, with
f
1
=
f
2
, a phase shift approaching
180°/
f
1
obliterates the wave by interference.