Cool! This is about an interactive display but initially I thought someone might have managed to make GOL into a physical automaton! Cells could physically sense neighbouring cell states and change their own states.. might still need a global clock to get coherent GOL behaviour but I think that would be fascinating!
Also GOL (2,3/3) is only one out of about 1024 possible 2d totalistic CA rules, some of the others have interesting behaviours too and would be fun to be able to explore in the real world :)
I'm sure a clever enough craftsman (not me) could do that, and even avoid the global clock. Each cell could send a "clock tick" to its neighbors whenever it updates its own state, and gradually adjust its tick interval toward the mean tick interval of its current neighbors. (Or maybe just snap quickly to the median tick interval of its neighbors.) After a few ticks all the cells would be synchronized.
To make the thing really "modular," I'd want the communication channels between cells (both the "I'm alive/dead" channel and the "clock tick" channel) to be something like sliding pegs that push into holes on the neighbors and can be sensed either mechanically or optically, not something that requires an electrical current to flow _between_ neighboring cells.
Adafruit sells a 4x4 Game of Life circuit board, which can be connected (permanently, with solder) to other 4x4 boards to make larger boards: https://learn.adafruit.com/game-of-life
Having to actually solder it to the other boards makes it not quite what I'm thinking of, but still pretty darn close.
Re counting 2D totalistic CA rules: it could be as many as 2^8 = 256 rules for "I come alive with (1,2,3,4,5,6,7,8) neighbors," times another 256 for "I stay alive with (...) neighbors," for a total of 63356 possible CAs. One _could_ add 16 switches to each cell, and have the cell use whatever rule is encoded by those 16 switches. That feels expensive, though, doesn't it?
Ah yes you're so right, a 'distributed' synchronisation method could work great!
I love the idea of mechanical sensing too! Would be cool if somehow the 3-neighbour 'grow' rule could somehow involve budding off a cell from the (or one of the?) 'parents' and transitions from 1 to 0 (cell death) could actually involve the disassembly of something! : )
Since GOL doesn't consider the self-cell, there are 9 possible values for the 'total' (0 to 8), and since there's both Birth and Survival, that's 18 bits in total, so 2^18 which comes to 262,144 possible rules! That is a LOT more than I thought there were! Cool! - makes me want to explore them again more thoroughly.
I was thinking that "I come alive with 0 neighbors" wouldn't make a sensible rule: it's not reasonable to have the whole universe strobing on and off every clock tick.
But "I stay alive with 0 neighbors" probably makes sense, so okay, multiply what I had said by another factor of 2 and call it 17 bits total. :)
