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.