Corrugated cardboard has the interesting property of being partially transparent in one particular direction: that of the corrugations. When you construct something with stacked slices of corrugated cardboard, you can see through it if you look at it the right way. When I was slicing topographical maps, it occurred to me to try to slice it in a direction other than horizontal. You lose the contours, but the roughness of the surface I thought might look interesting if back-lit. It ends up looking quite dynamic when you walk past it:

To make this lamp, you will need access to a laser cutter, some corrugated cardboard, a $75 LED panel, and some 2×4 lumber.

Step 1: Design

LED panels meant for ceiling tiles are inexpensive and provide light over a 4 square foot area. That size is easy enough to laser cut pieces for and will preserve lots of detail. It does make for rather a lot of cardboard, though: 132 pieces consuming 8 sheets of 2'×3' cardboard. Choosing a design that is REALLY topographically interesting (e.g. a mountain) may consume too much cardboard (and cause you to stand in front of the laser cutter for rather more time than you intended). I chose part of the Grand Canyon; a place I've never been to but have always been fascinated by.

Step 2: Make a Box

Carefully measure the LED light panel. The one I bought had a transformer box on the back 45 mm (~2") deep. I designed it so the frame could be made out of 2×4 construction lumber, but I exploited my access to the Pier 9 workshop and dimensioned some white oak to a similar size. I cut a dado 26 mm deep and 11 mm wide, 30 mm away from one edge as shown. I did this with multiple passes on the table saw. Cut miters on each end so the box is 604 mm in the longest dimension. Slot the LED panel into place, and glue it all up. Thanks to Trent for excellent advice; these were the best miters I've ever managed to make.

You'll need to buy a power cable if you don't have one lying around.

Step 3: Get STL File and Modify

If you want a terrain map, like the one I used, check out my other instructable. All I plan to do here is show how I modified one of these to fit in a 2' × 2' space, not how to make them in the first place. But of course this idea would work for any STL file that has interesting texture - a face, geometric shapes, whatever.

I got an STL of the Grand Canyon from Terrain2STL. It had two main issues: it was not square and the base was too thick, so I needed to trim bits off it. I did this in MeshMixer by importing the mesh and making two plane cuts to make it square and shallower. I could then save it as a new STL file.

Step 4: Size and Slice

Once you have a square STL, open it in 123D Make, size it to the exact dimensions you need and slice it. Don't exaggerate the vertical dimension too much, or you will be cutting dozens of sheets of cardboard and not much light will get through. If you want to reproduce this spotlight exactly as done here, I have attached all the cut files I used in the EPS format. I advise making your box first, measuring the exact dimensions, and scaling the profiles accordingly. The fit needs to be as perfect as possible.

Set the line thickness to 0.001" (which the Epilog lasers I was using recognize as cuts rather than rasters), and enable color mapping. Set blue up to cut (whatever setting is appropriate for that on your machine) and red up to cut but at maximum speed and a MUCH lower laser power, so it only very lightly scores the surface.

For speed of assembly, arrange in order as they come out of the laser cutter and put together using spray adhesive.

Step 5: Hang and Enjoy

This fixture will work best if it is positioned somewhere that the light is illuminating something else you want highlighted. It is not bright except directly opposite, so set it up to spotlight something else in the room.

If you are so inspired as to make one of these, post a picture and I'll send you a one year premium membership to instructables.com.