What you actually need for it is a 2-dimensional display the bigger the better. You could go for an LED matrix which needs a lot of wires - or a TV screen.
The algorithm is pretty simple - all you need is two 2-dimensional arrays for all the cells, may they be dead or alive. Why two of them? Well, one for the current generation and one to calculate the next one.
So you actually need two microcontrollers: the one from the Arduino and the ATmega8. The Arduino sends its data through RS232 to its slave (yellow wire).
Unfortunately, both chips need a 16 MHz quartz.
The Arduino has to reset the slave and wait for about 2 seconds before sending data to it.
2. There is still space left in the first controller. So why not letting it do the display itself? Yes, you can!