Here's a great video I found on YouTube. A 2009 graduate installed 64 RGB LEDs and 8 TLC5947 drivers along with an Arduino Mini, in a mortar board cap. I don't know the actual dimensions of a typical cap, but 8" per side seems about right. The project in this video could be easily duplicated by using OctoBrites, which are 4" modules containing 8 RGB LEDs spaced 1/2" apart. Cool stuff!