A simple example
We can generate digit images by
simulating the physics of drawing.
A pen is controlled by four springs.
The trajectory of the pen is
determined by the 4 spring
stiffnesses at 17 time steps .
The ink is produced from 60 evenly
spaced points along the trajectory:
Use bilinear interpolation to
distribute the ink at each point
to the 4 closest pixels.
Use time-invariant parameters
for  the ink intensity and the
width of a convolution kernel.
Then clip intensities above 1.
We also learn to set the mass,
viscosity, and positions of the
four endpoints for each image.