In this video Nick Johnson demonstrates his tiny Minimatrix project and wrote a detailed explanation describing the build:
While minimatrix is in principle a pretty simple device, there’s a surprising amount of detail that goes into getting it right – and some interesting lessons to be learned in designing and programming it. I thought I’d detail a few of them for the benefit of anyone building something similar – or simply for interest.

How does a single 3v battery keep it running for up to 24 hours?
A common cr2303 has 230mA capacity. 230mA 12 hours, gives 19mA per hour used. Consider that the microcontroller is asleep between timer interrupts, and only 1 row of leds are on at any given time, or less, It’s quite easy. Additionally, when less leds are on a row, there is a timer which disables them after a certain amount of time, to maintain equal brightness across them.