A lumographic ("light-drawing") lens makes a picture by concentrating and diverging light rays to make bright and dark patches in the image. It produces the same hypnotic play of light that you see under moving water on a sunny day, and the same way -- an undulating surface bends light rays -- but with quite different results:
(mouse over these two images to see video; better video to come once I figure out how to kill the videocam's confused autofocus)
The trick is to find a lens shape that rearranges light rays just right to make a desired picture. More than one lens shape will work, so I find the smoothest one, which will be the easiest to fabricate. The result is a little like a funhouse mirror:
A lens (left) and the image it throws on the wall (right).
Speaking of which, one can also make lumographic mirrors:
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