1/ Tragically, the famous mathematician John Conway has recently passed away to COVID-19. To commemorate his life, here's a thread about his most famous creation, the Game of Life, which raises many provocative questions about the nature of complex systems.
2/ The Game of Life is a system consisting of an infinite grid of squares, that can be either black (alive) or white (dead). Every time step, the squares evolve according to three simple rules:
3/ 1) Any live cell with two or three live neighbors survives.
2) Any dead cell with three live neighbors becomes a live cell.
3) All other live cells die in the next generation. Similarly, all other dead cells stay dead.
2) Any dead cell with three live neighbors becomes a live cell.
3) All other live cells die in the next generation. Similarly, all other dead cells stay dead.
4/ With these three simple rules, you can get all kinds of emergent patterns: some stay still, some oscillate, some move across the grid, and so forth.
5/ For example, the glider pattern will fly forever:
6/ You can build a "glider gun" that will spit out infinite gliders:
7/ And you can even make a "breeder" that will blaze a trail across the grid, spawning glider guns in its wake, each of which will spit out gliders forever:
8/ Though the Game of Life has been studied for decades, people are still learning more about what you can do in it.
9/ For example, in 2010, a pattern was discovered that can simultaneously clone and delete itself... every 34 million generations! It uses an "instruction tape" that guides the cloning of the pattern, including the cloning of the tape itself.
10/ And you can even build a universal Turing Machine in the Game of Life, complete with ticker tape. Thus, you can compute *any* computable function within it.
11/ If you believe the brain to be a computer (in the classical sense), you could therefore theoretically simulate a brain within the Game of Life.
12/ And since the rules for running the Game of Life are themselves computable, you can also build a simulation of the Game of Life *within* the Game of Life:
13/13 Many lessons to learn from this, but to me it's a humbling reminder that you can get amazingly complex and unpredictable behaviors from the simplest parts. #conway #gameoflife
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