A review of Conway’s Game of Life

Okay, it’s not actually a “review” this time. But then Conway’s Game of Life isn’t quite a “game” in the regular sense.

The subject of today’s post, sort of. And yes, that is Anime Pin-Up Beauties ’99 lower in the menu. When you see a gem like that on the Internet Archive you have to get it, you know.

Strangely enough I’ve already written about this thing on the site without realizing it. Three years plus ago, I reviewed the entire Windows Entertainment Pack, a set of early 90s games and programs contained on four different releases. One of these was a game titled LifeGenesis, which I tried out again after reinstalling my virtual machine with Windows 95:

WHAT the fuck is going on

When I played LifeGenesis, I didn’t really understand what I was looking at and assumed it was a broken two-player Go or Reversi spinoff of some kind. Granted, it was represented as a two-player game that I thought would be set up as player vs. computer like most of the other such games in these packs, but that doesn’t change the fact that I just didn’t get what was going on and didn’t read the game’s documentation, which actually explains what it is: a very limited Windows-based version of Conway’s Game of Life, a sort of program (or cellular automaton as he called it) created by mathematician John Conway in 1970. I’d explain the rules, but better to let the man himself do that:

The gist is that on a potentially infinite grid, you can place “live” cells as you would pieces on a board, and their status changes based on their position and their neighbors. Since the game continues tracking these changes from step to step, you’ll end up with a morphing pattern that might either die out completely, get frozen in a certain position, or bloom out into a progressively larger pattern.

Throwing down random clumps of blocks like I did the first time I played LifeGenesis can be pretty amusing for a few minutes, but the most interesting patterns to me are the symmetrical kind, easily produced by a symmetrical starting pattern of live cells. While some of these patterns die out or freeze in place after several rounds, others have surprising properties. Take a row of 10 live cells, which you might not expect anything interesting from: you’ll end up with a changing pattern going through several cycles that repeat infinitely:

Part of the repeating pattern

There’s a lot more you can do with the Game of Life, but LifeGenesis, as interesting as it must have been to people who knew about this in the early 90s, is unfortunately restricted with a finite game board. This board is meant to be used in matches against other human opponents I guess, even if there is a difficulty option featured (though the computer opponent still seems to be absent, so I have no idea what you’d do with this game’s difficulty setting.)

Today, there’s a far easier and better way to play Conway’s Game of Life than running LifeGenesis on a virtual machine: you can instead visit this site and run patterns on an effectively infinite grid, meaning you can get far more interesting and complex results than you would otherwise on that restricted game board.

Again, I went straight for the symmetrical patterns, trying out various starting positions. Most of these didn’t produce very interesting results, but a few turned out some beautiful patterns like the one above, just the 59th round (iteration? I want to use that word but I don’t know if it’s correct here) out from a pretty simple cross-shaped starting pattern. Some of these results look strangely human-created even, like these pixel art ghosts from earlier in the very same pattern progression:

A symmetrical starting pattern will always result in symmetrical results as you’d expect, but the true chaos begins when you go asymmetrical. Again, most of the patterns I placed down fizzled out pretty quickly or resulted in a few fixed live cell patterns (the 2×2 square, for example) or infinitely alternating or “spinning” ones (the 3×3 line.) A few were far more interesting, producing increasingly growing explosions of live cells that create fixed patterns and destroy them again as they keep growing and reacting to their surroundings.

Here’s a pattern that I thought was about to settle down — almost everything on the screen above is a static pattern that resulted from a pretty small and simple starting position (though one I don’t remember, honestly.) Everything except this bit:

That five-cell pattern is known as a “Glider” because unlike nearly every other pattern, it endlessly glides across the grid while maintaining its form, going through a few repeating cycles. This particular glider is headed “northwest”, or towards the upper left corner of the grid, about to run into the static six-cell pattern above it. The result:

Another explosion that “invaded” those static patterns down below and kept the game going. This is one of the interesting things about the Game of Life. From what I can gather, its outcomes can all be mapped out since it follows just a few strict rules, but for a human watching these changes play out, it all really feels chaotic, in a few situations like the above like anything might happen..

Of course, far smarter people than me have done far more interesting things with the Game of Life than I could have imagined without finding them on YouTube:

I’m not a huge fan of that overused dramatic backing track, but man these are impressive. This “game” has been around for over fifty years now, so it’s no wonder people with more mathematical minds have been coming up with such incredibly elaborate and massive patterns.

That brings me to the last point about Conway’s Game of Life and maybe the most interesting: the fact that Mr. Conway himself didn’t seem to think much of it. To Conway, the Game of Life was sort of a trifle, something to play with, that he sent to a friend to write about in a Scientific American column. After it exploded in popularity, he knew he’d be remembered by most people for this trifle, which wasn’t all that impressive to him and was greatly overshadowed by his other work as a mathematician.

Yet he also came to terms with that, and for good reason: looking through conversations about his game, I’ve found a lot of people citing it as the reason they got interested in programming. I can understand why, even if I’m a humanities major and not at all into math beyond some of the interesting concepts I’ve stumbled upon along with the other non-mathematician masses like the Mandelbrot Set. Part of the appeal of both of these concepts to me, and I think to a lot of people, is how they show complexity, and even infinite complexity, can be revealed by something so seemingly simple as John Conway’s game with just a couple of rules or Benoit Mandelbrot’s equation.

Or maybe I just like the nice patterns. I don’t think I have anything at all to add to the talk about the Game of Life, not coming from my professional background that has nothing to do with math beyond estimating potential damages and worrying about project budgets in dollar amounts.

Anyway, this is just something I’ve been messing around with lately. I hope my recent less regular posts have been interesting — I’ll be getting back to the more standard kind soon, unless I come up with more to ramble about. Until then!