@NathanOsman I think the answer is neither. But I don't use that kind of thing often. If you want to make your second version, you can use something like this:
On the car, the "ground" is just the metal of the car itself. Provided the ground plane is larger than (I think) 1/4 the wavelength all is good - without a real earth ground.
Had a situation many years ago where we had a portable mobile two-way radio in UHF with an antenna with a magnetic base intended for use on cars/trucks. We needed to use it without the car or truck (two stories up, out of the window on a masonry building.) No earth ground, and no ground plane. The dealer gave us a square piece of sheet steel somewhat longer than the antenna. Antenna on the sheet, balanced on the window ledge, prblem solved.
Microprocessor, serial shift registers for input (initial state) and output (LEDs,) LED drivers. You have a lot to learn and do before you are finished.
Then you've got a lot of work ahead of you. For each LED, you will need a circuit that counts how many other LEDs around it are lit. You will need to use the output of that to decide whether to turn the LED on or off. You will need 25 of those things to cover all LEDs. Seems to me like you would end up with a fairly large and complicated circuit board.
I'd start with one LED, and a hand full of switches to set the number of surrounding "live" cells. Get the logic for that straight, then build 25 of them.
Shift registers. 25 in to serial, to a second shift register that has 9 outputs. Connect those to your logic, and shift the result back to a register with 25 outputs to drive the LEDs.
@ADG Counting the number of set bits in 8 inputs doesn't reduce to any simple combination of AND and OR gates. But there's a number of ways to generate arbitrary truth tables, using either MUXes or ROMs. Or if you want to serialize the problem, consider shifting the bits representing the state of the neighbor cells across the CE pin of a counter.
Probably the cheapest way to do it with SSI/MSI chips.
I'm not sure if there's a clever way to figure out which cells are neighbors to simplify figuring out which signals to connect. Might be back to ROM or MUX logic.
@ThePhoton suppose if input are i0,i1,..i7 (surrounding bits) then I was thinking of taking full adder for i0,i1,i2 (one is Cin) and similarly for i3,i4,i5 and then half adder for i6,i7 [All these using 7486,7408,7432] then addign first two sums with 7483 and then again with 7483