This is a (moderately) simple Arduino project that is a spectacular display from LEDs - that you can wear on your head! It also uses a program that is not intricate at all, so you can modify it for different patterns and cycles. It's also a great first or second project for people new to Arduino. And, of course, it looks great in the dark!
(I know the video isn't ideally situated; I'll try to fix that soon)
Step 1: Parts List
You will need:
A hat (of course)
24 LEDs for the version pictured - Radioshack sells a bundle of red, yellow and green LEDs, which is what I used x2
9V connector or plug
Fishing line or string
Very small breadboard
Arduino Uno, Leonardo, etc.
Step 2: Parallel vs. Series
It might be simpler, but building the circuit with the LEDs in series (with the positive leads connected to the negative ones of the next; 5th picture) requires more voltage than the Arduino can provide. Two LEDs work, but for this design with three LEDs I used a parallel circuit. When connected in this way, like the in first four pictures, the Arduino can power at least four LEDs at once, although they are slightly dimmer.
Step 3: Construct the Ground Circuit
Since the Arduino Uno has only 3 ground ports, you'll need a circuit that you can plug all 8 LED strips into. With a super-small breadboard (this one is 5x10), plug one wire into the ground pin on the Arduino and a row on the breadboard, and two more wires from that row into two other rows.