Here's a video of it in action. They're tricky to capture video of (particularly when using a cheap digital camera), but it gives you a rough idea:
This is an incredibly simple project to put together, thanks largely to the LEDs: I use RGB LEDs with color-changing circuitry built right into the package. You just provide power, and the LEDs cycle through red, green, blue, and various combinations thereof. One aspect of these LEDs is that the timing is slightly different in each one, so while they start out in sync, they quickly fall out of phase. I consider this a feature, not a flaw, as it results in the emergence of interesting, seemingly unpredictable patterns.
No soldering is required, just some crimping and a bit of hot glue.
The parts are easy to obtain online, but I also offer kits through Make Magazine's online store, the MakerShed, for $15:
Step 1: Parts and Tools
The screen: I used 4 x 3 piece of scrap translucent white plastic. Velum from the paper department of your local art store works perfectly as well.
5 x 4 matboard frame with a 2" x 3" window: You can get a piece of black mat board cut to these dimensions in any framing store for a few bucks, or cut one yourself from suitable material, such as stiff black cardstock.
Battery case for 2 AA batteries w/ wire leads and power switch: These can be purchased online from Jameco, part #216120, and can likely be found at Digikey.com or Mouser.com as well. Similar battery holders can also found at Radio Shack, but you may have to solder a simple power switch into the circuit yourself.
3 RGB color-changing LEDs: I get these here: http://stores.ebay.com/Amigo-Of-China. Look for "5mm RGB LED Slow Colour Change." Make sure you get the clear ones, as the diffused ones don't work as well for this specific project (but you can do other cool things with them!) Everything on this store seems to come with free resistors, which you don't need for this project, but hey, free resistors.
2 butt splices: (tee hee... butt splices). These can be found at Radio Shack; something in the range of 18-20 gauge or thereabouts works well. I use the non-shrink-wrap-coated ones, but the coated ones should work fine. You can also get these from Jameco, part #494469, but the minimum order is 100.
Also shown in the picture: Glue Dots. These come with the kit, and are used as an alternative to hot glue to attach some parts together. These can be found in a craft supply shop (you should get the largest, tackiest (stickiest) ones they have), but a hot glue gun works just as well for these steps, and is nice to have anyway when it comes time to "customize" your LED artwork.
You will also need 2 AA batteries, and some scotch tape.
TOOLS (not shown)
Wire clippers and strippers: these may be needed for cutting and trimming the wire leads on the battery case.
Scissors or similar cutting implement if you are going to cut your own screen or mat board.
Hot glue gun: As mentioned above, glue dots can be used instead of hot glue for attaching some parts, but the glue gun is useful for the optional (but highly recommended) step of customizing your artwork.
Step 2: Assemble the Frame
Next, tape the left and right edges of the screen to the back of the frame. Make sure the tape does not overlap with the window, or it will show through when the screen is illuminated from behind.
Step 3: Prepare the LEDs
Bend the remaining 2 LEDs in the same way.
Step 4: Crimp the LEDs
It's very important that you remember which are the positive LED leads; you may want to mark this splice with a small piece of tape. If you get confused, each LED lens has a little flat spot next to the negative lead. Now gather the negative leads, and place the other butt splice over all 3 leads. Again, give it a good squeeze, being careful only to crimp the LED side of the splice.
Step 5: Wire LEDS to the Battery Case
Now gently bend the leads at each splice, so it looks like the picture. It is very important that the two splices never touch, if they do, it will prevent your LED Art from lighting up, and quickly drain the battery.
Step 6: Test the LEDs
The three LEDs should immediately turn on, and begin to change color. If they don't, here are some troubleshooting tips:
If some but not all of the LEDs turn on, you probably have one or more LEDs in backwards; that is, you didn't line up all of the positive LED leads. You may need to pull off the crimp with a pair of pliers, or cut it off \with a wire cutter. There should be enough extra LED lead to re-crimp, but you'll probably need more butt splices, which can be found at Radio Shack.
If none of the LEDs light up, you may have reversed all of the LEDs (i.e., attached the red wire where the black wire should be, and vice versa). Rather than pull or cut the splices apart, put the batteries into the holder in reverse.
Still no luck? It could just be a bad connection. Try cutting off the crimps, re-stripping the wire, and re-crimping w/ new butt splices.
Step 7: Attach LEDs to the Case
Gently peel the strip of glue dots open, being careful not to touch the blobs of glue, or get them stuck on anything (they're like way sticky). Cut the backing so you have a single dot, and affix it to the case, near the switch.
Press firmly, and peel off the backing (if needed, use your finger to help the glue dot stick to the case, but try not to touch the glue more than necessary).
Now firmly press one of the crimped splices (it doesn't matter which) against the glue dot.
Step 8: Test the "Display"
Take a look at the front of the piece, and see how the colors and patterns change over time. You can adjust how your piece looks by gently repositioning the LEDs.
Step 9: Optional (Recommended): Distort the LEDs With Hot Glue
Plug in your glue gun and give it a few minutes to heat up. If you're a kid, you definitely need to get some adult supervision for this part!
Carefully drizzle small amounts of glue on the LEDs. Let the glue cool, and see how it looks when projected against the screen. Give it a few minutes to let the LEDs cycle through their various colors. Feel free to experiment, as it's easy to peel the cooled glue off the lens and try something different!
Step 10: Attach the Case and Frame
You now have a one-of-a-kind piece of LED artwork... enjoy!
I really like working with these LEDs, and they have a lot of creative possibilities. Here are some links to flickr sets of projects I created with them in the past, which this Instructable is based on: