I'm interested as well in implementing Conway's Game of Life but I wonder, what are the applications of this system in computation? Can a Turing Machine be constructed with this system?
Not only is the answer "Yes, a Turing machine can be constructed out of GoL, demonstrating that GoF is universal," but given that GoL is itself a computation, the reverse is true: You can build GoL out of a Turing machine.
I took a stab at it a few years ago. My strategy was to start with a very basic Turing Machine, and then write a compiler that compiled a more sophisticated Turing Machine out of a simpler Turing Machine.
For example, when I wanted cells to have a value and a tag, I wrote a compiler that translated every possible combination of symbol and tag into a single flat space of symbols.
I stacked compiler on top of compiler until I had a Langdon's Ant with various programming conveniences, and I wrote a 9-cell GoL using my Langdon's Ant.
The whole thing compiled to a very simple TM with millions of states, but it worked. I did not make it practical enough to ever manage a GoL big enough to emulate a Turing machine, but I feel that I did enough to get some practical experience with something that is straightforward in theory.
> what are the applications of this system in computation?
If you mean "applications" in the practical sense, there are basically none, but that's part of the fun. GoL is fascinating in part because it's pretty much useless, yet has been studied extensively by bored computer scientists over the decades.
I took a stab at it a few years ago. My strategy was to start with a very basic Turing Machine, and then write a compiler that compiled a more sophisticated Turing Machine out of a simpler Turing Machine.
For example, when I wanted cells to have a value and a tag, I wrote a compiler that translated every possible combination of symbol and tag into a single flat space of symbols.
I stacked compiler on top of compiler until I had a Langdon's Ant with various programming conveniences, and I wrote a 9-cell GoL using my Langdon's Ant.
The whole thing compiled to a very simple TM with millions of states, but it worked. I did not make it practical enough to ever manage a GoL big enough to emulate a Turing machine, but I feel that I did enough to get some practical experience with something that is straightforward in theory.
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Turing Machine in GoL: https://www.youtube.com/watch?v=My8AsV7bA94