A map of the territory
Recently while doing some “serious research” on Wikipedia I stumbled across Conway’s Game of Life. Over the past month I’ve been trying to figure out what makes it so interesting to me. I’m not really part of the cohort that would be expected to like this sort of thing—I have only a limited fondness for recreational mathematics, and I’m not part of academia. But Conway’s Game of Life holds a strange fascination for me. On the surface it seems just a silly thing to do with computers. But I think there is something much, much more profound going on here, and it touches on something I’ve been preoccupied with for as long as I can remember—the definition of, and limits of, art.
This essay will be in two parts: this installment will be a road map to the phenomenon of Conway’s Game of Life (which I will just call Life); the second part is where the real meat will be, and if you are already familiar with Life, you probably won’t learn anything by reading this, and you might just want to skip straight to the part two. But if you aren’t familiar with it, let me describe Life for you. In 1970, John Conway, a mathematician and computer researcher at Cambridge, published a paper in Scientific American as part of Martin Gardner’s widely influential “Mathematical Games” column. In this paper, Conway described a game he had created the previous year. It is a zero-player game; a person plays it by creating a set of initial conditions and watching developments unfold. The rules of the game are absurdly simple. Imagine a piece of graph paper. Color in some of the squares; they are called “live.” All the uncolored squares are “dead.” Then, follow these rules:
Any live cell with two or three live neighbors survives.
Any dead cell with three live neighbors becomes a live cell.
All other live cells die in the next generation. Similarly, all other dead cells stay dead.
For each turn of the game, repeat these rules, and watch what happens. The fastest and easiest way to understand how the game works is to play it. That is quite easily done, and you can play Life online. Go ahead—take some time to goof around with it; if you do, you will quickly find that Life is capable of producing some very interesting, pleasing, and ASMR-esque patterns. Here is a “triple pseudo still life.” This pattern will remain in this static state forever when the above rules are applied.
This next pattern is an oscillator—it comes back into the same configuration after a few steps.
Here is a glider—a small pattern that repeats itself every four steps, and “travels” down the playing field as it does so. (Note: this glider pattern is EXTREMELY IMPORTANT. We’ll get to why later.)
Here is what is called an R-pentomino. This small pattern goes completely nuts and takes a very long time to calm down.
Some patterns in Life interact with themselves in intriguing ways. This is Gosper Glider Gun (Bill Gosper, 1970)
—a pattern that continuously “shoots” gliders out of itself.
Now, what happens when two or more of these gliders crash into each other? If you have a moment, create this pattern in the online Life game mentioned above, and watch the result.
In this example, three gliders came together to make what is known as a heavyweight spaceship. This sort of thing is called glider synthesis among Life enthusiasts, and here’s where the game starts to get very elaborate.
Using a setup of guns, spaceships, and other things like reflectors and eaters, you can make complicated patterns that will interact with each other. A gun “shoots” gliders toward a reflector, which “bounces” them toward other gliders, which “bump” into each other and synthesize into still lifes, which, when smashed into by other gliders, turn into spaceships, which smash into gliders to produce guns, which produce gliders that smash into each other to produce rakes, which move across the playing field while emitting still lifes, oscillators, and other spaceships and rakes . . . ad infinitum. For fifty years, people have been designing these constructions. The first, and one of the most elegant in my mind, is Breeder (1971), by Bill Gosper, which you can view here. But Breeder is just the tip of the iceberg. Enormous constructions of interlocking parts have been built in Life, spaceships such as Mosquito 1 (Nick Gotts, 1998) and Waterbear (Brett Berger / Ivan Fomichev, 2014), and the absolutely immense Gemini (Andrew Wade, 2010), which is made of nearly 850,000 cells and which is so big that my desktop computer can barely run the RLE file that would allow me to watch it in action.
Gemini operates using a mechanism called a “slow salvo”—a stream of gliders, spaced carefully and exactly, that are “read” by the object at the end of their travel path, exactly like a memory tape is read by a computer. There are other ways in which Life can emulate computer systems. From Wikipedia:
if two gliders are shot at a block in a specific position, the block will move closer to the source of the gliders. If three gliders are shot in just the right way, the block will move farther away. This sliding block memory can be used to simulate a counter. It is possible to construct logic gates such as AND, OR, and NOT using gliders. It is possible to build a pattern that acts like a finite-state machine connected to two counters. This has the same computational power as a universal Turing machine, so the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints; it is Turing complete. In fact, several different programmable computer architectures have been implemented in the Game of Life, including a pattern that simulates Tetris.
But the ultimate Life creation—and the one that hurts my head just thinking about it—is Metapixel. This creation, designed by Brice Due in 2006, is a construction which can replicate the actions of Conway’s Game of Life on its own. There is a short stream of spaceships that move around the perimeter of this pattern, and if the pattern is repeated across the playing field, the spaceships interact with the edges of the adjacent patterns in such a way that they can turn “on” or “off” other streams of spaceships on the inside of the pattern. For a visualization of this, watch the video at the beginning of this New York Times article
. There is some sort of eldritch, Lovecraftian horror about this video—a vertigo-inducing, fever dream quality that arises while watching the view slowly pan out, and speed up, until you realize that this could go on forever, with no limits—one could conceivably build a meta-metapixel using tiled metapixels, and a meta-meta-metapixel using tiled meta-metapixels, and a meta-
Life can be taken very seriously. There is a forum which gets extremely esoteric and arcane, and the official wiki is full of jargon like this:
The blinker can function as a transparent catalyst in a certain reaction where it is converted into a traffic light predecessor, which a fishhook (or another catalyst that engages in the same type of catalyzing reaction, such as an eater 2) then converts back to a blinker in the same position. This rephases the blinker, so it can only be used in odd-period oscillators, such as 66P13 and the p47 pre-pulsar shuttle.
That’s not a problem at all, except when the descriptions of Life begin to get bizarrely metaphorical. Remember that anything in Life happens on a cellular level; yet people talk about “spaceships” and “oscillators” is if they are one object. I did, myself, earlier, when I used all of those scare-quote verbs. The individual cells in Life interact with each other according to the rules of the game, but any action in concert or en masse is an illusion. Yet people talk about the game as if it were a microcosm of actual life—the carbon-based kind. The NYT article referenced above contains several of this kind of erroneous take. The worst of them all was by Brian Eno (!), who says
The second thing Life shows us is something that Darwin hit upon when he was looking at life, the organic version. Complexity arises from simplicity! That is such a revelation; we are used to the idea that anything complex must arise out of something more complex. Human brains design airplanes, not the other way around. Life shows us complex virtual “organisms” arising out of the interaction of a few simple rules—so goodbye “Intelligent Design.”
Um . . . ? I don’t know how an intelligently-designed system is proof against the idea of intelligent design; besides, Life isn’t alive! Some aspects of the game mimic some aspects of the sort of thing that happens in petri dishes, but that is only a metaphor. The colored squares in Life are not alive, no matter what its proponents might seem to be saying—and this is the point where I lose my patience with the whole thing. But— if Life isn’t alive is it at least something else? Is it art?
And that, readers, is the question that I will address in my next essay. Until next week, then! If the screenshots and gifs above struck you with inspiration, you can very easily dive in and start producing your own Life masterpieces. There is a freeware called Golly which can be used to create and run patterns in Life; it is the standard method of interacting with the game, and I highly recommend it if you want to explore Life further. Also, here is a very trippy video of Life patterns made of enormously large X and square shapes, and here is the result of trying to find Life patterns that will turn into semblances of famous artworks (spoiler: it’s very tricky, and maybe impossible).
And . . . here, you can turn your Wordle score into a pattern in Life, because why not?!
Swiped from the Wikipedia entry.
For reasons that will become apparent, I will be treating the names of these patterns as the titles of artworks, citing their creators, and referencing the date of their creation.
The article is behind a paywall, but you should still be able to see the video.