the harmonograph

This is a simulation of a four pendulum harmonograph using logo. The successive positions are calculated using this formula:

x = ke-rt[sin(f1t + p1) + sin(f2t + p2)]
y = ke-rt[sin(f3t + p3) + sin(f4t + p4)] 


where
k = 70 (makes the drawing fill the screen)
r = .0001 (the "damping" factor)
f1,f2,f3,f4 = pendulum frequencies
p1,p2,p3,p4 = phase angles
t = time (0,1,2,3,...,5000)
The frequencies are assigned randomly from 0,1,...,10, the phase angles also but from 0,1,2,...359. These 8 numbers appear in the box for each drawing.

Further information:

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