A hidden picture lamp, utilizing lithophanes. Note: this does not use an actual hidden picture! It is a piece of plastic where the thicker spots absorb more light (black) and the thinner spots absorb less light (white) giving a photo effect.

Lithophane source: http://www.thingiverse.com/thing:74322

Less work / More work:
Less: A remix (Remix 1) is included with a single level LED tower. This remix cuts the lamp height in half, and thus reduces the build time.

More: Once you are done with developing and printing the lamp there is a Round !! (Yes, Round "double exclamation point"). Cut off the IR remote control sensor and replace it with a WiFi sensor. This will enable you to control the LED strip with your WiFi connected devices, such as your cell phone! Here is a demonstration: https://youtu.be/QEek-LAnwTg

The lamp:

(1) Use this website to make the lithophanes: http://www.thingiverse.com/apps/customizer/run?thing_id=74322 (Note: a few of us could not get this to load in IE; I had to use Chrome). Here is the exact process I used:

• Image:
  • Picture Shape: Square
  • Picture Orientation: Horizontal
  • Pane Size: Large
  • Invert Colors: Checked
• Adjustments:
  • Include Hole: No
  • Hole Diameter: [Doesn't apply]
  • Layer Height: 0.2
  • Number of Layers: 20
• Slicer (KISSlicer to be exact)
  • Height from 4.4mm to 3.2mm

If the customizer errors for you, see user "dlee_maker" comment on an alternative lithophane generator.

(2) Print your lithophanes and scale to 76 x 76 x 3.2 mm. (Change the print height in your slicer and the x, y dimensions should be correct.) Printing anywhere 0.1mm - 0.2mm is great with 100% infill.

(3) I used ABS; the LEDs get the structure up to 50-60C. PLA will work by limiting the LED brightness if it gets much hotter.

(4) If you normally use "ABS juice", use a glue stick this time. Cleaning the residual slurry off the flat side will be unsightly (as it is the outside part of the lithophane.)

(5) Print the lithophane support structure at your standard settings with no support required. 100% infill is not required for these.

(6) The LED tower is glued to the base with something strong such as J-B Weld.

(7) The shown LED strip: http://www.amazon.com/dp/B0040FJ27S/ref=sr_ph?ie=UTF8&qid=1434942772&sr=1&keywords=LEDwholesalers

Here is a how-to video if you need: https://youtu.be/yYU1c8UoDfI.

The WiFi LED Driver (OPTIONAL!):

Materials (for exact copy; substitutes would surely work):
(1) LED Strip + it's power supply (link above)

(2) Particle Photon (http://www.particle.io)

(3) D24V10F5 Voltage Regulator (http://www.pololu.com)

(4) 3 ZTX689B NPN BJTs (http://www.digikey.com)
I highly recommend these transistors over TIP31s that people typically buy. These have a very low saturation current, and they support this power application sufficiently.

(5) 3 resistors ~330 ohms (driving this with 3.3V PWMs signals from the Photon)

(6) (Optional - Highly Recommended) Heatsinks for the BJTs
Power transistors get hot, and should be used with heatsinks (even TIP31s). With the heatsinks, the transistors measure at ~45C passing 0.4A each.

(7) (Optional) Breadboard, Heat-shrink Tubing, Solder

(8) (Optional) Web server for Photon to talk to (I'm using a BeagleBone Black.)

(9) WiFi Device (Cell Phone, Computer, iPad, etc)

There is a photo schematic for how to connect these components. The website's javascript and photon code are fairly straightforward (assuming you have a slightly technical background.) Here is my photon code and a JavaScript example: https://onedrive.live.com/redir?resid=8020F0E348C88BBD!93112&authkey=!AMioGTxVfcdw1gA&ithint=file%2ctxt

[Update: 10/25/2015 - Be sure to use pull down resistors on the base of each transistor. Just use ~10k ohm resistors on each base to the ground.]