Thanks for the response! Sorry, I have just been working so closely with this project, that I sometimes forget that they don't really make sense unless you are familiar with them. I have edited the first post and put in a definitions section. If there is another definition that is not clear, just let me know and I will clear them up as well.
Yes, so there is a set pattern, that is repeated each rotation. The theory of persistence of vision makes the individual parts of the pattern look like a full image. Here is a wiki on the topic: http://en.wikipedia.org/wiki/Persistence_of_vision
As for timing, I only track the time per revolution, which is triggered by an infrared emitter and collector. My original plan was to use a magnet and hall effect sensor, but the hall effect sensors that I ordered were not sensitive enough. I had the infrared parts sitting around so I made adjustments and used that for timing instead.
The Arduino is manually switched on, and the data is stored in flash. The main problem with the Mega 2560, is that only a few images can be stored in flash at start-up. At setup, the images are read from flash into the Quad Ram chip where the data can then be pushed out to the LED drivers. The order of images and duration is preloaded at setup and is the same every time the Arduino is powered up. This can be reset each time a new sketch is uploaded.
All power is mounted to the hub/spokes of the bicycle wheel. The Mega 2560 and all of the LED's are powered from the hub mounted battery pack. The run-time depends on the actual images that are being displayed. For example white colors suck the life out of the battery pack much faster than a primary color.
I do have to say that from the side at night, my bike is WAY more visible. Generally riding at night, the front is visibly because of a headlight on the handle bars and the back is visible from red/yellow flashing lights, but it is fairly difficult to see a cyclist from the side. That is not the case with this project.
That should shed some light on your questions (pun intended).