This demo simulates a Harmonograph (see also Lissajous curve), a device that traces the motion of a swinging pendulum, based on the following equations:
x = sin( phasex + cycle * frequencyx ) * amplitudex * (1-dampingx)cycle
y = sin( phasey + cycle * frequencyy ) * amplitudey * (1-dampingy)cycle

X frequency
Y frequency
X phase
Y phase
X amplitude
Y amplitude
X damping
Y damping
Draw from cycle...
... to cycle
Points per cycle

Animate whatever parameters you want in the code under function AnimateParameters()