This is excellent! What is needed to pull off a simplified version of this with a plain Arduino Decimal? I have an 8x8 matrix and got Life running on it without the Max chips (uses every free output). What would be used to add appropriate clock capabilities to an Arduino board? What else would be missing? Again, nice work!
The easiest way to add a real time clock is to use a 1307RTC clock chip as this project actually uses. You'll need a couple of IO lines for the interface though so, I'm not sure you'll have enough with 16 lines tied up for the matrix.
You can try keeping track of time in software using timer interrrupts, but it puts a lot more burden on your code.