This pattern is called Row Your Boat. As one of the strips starts to get brighter, a nearby strip will join in the fading. After completing a fade cycle, they start switching colors. There is a random strobe thrown in there as well. The first 10 seconds are with a diffuser (piece of paper), the last 10 seconds are without. The final panel will use a diffuser.
Initially I tried to get a LCD screen working with my Illuminato based Arduino. After a couple of attempts I realized two things: 1. The Iluminato is not ready for prime time. and 2. I burned out the LCD. So I decided to move on to the LCD strips I have from Sparkfun.