# Eli5: What’s the significance of Conway’s Game Of Life?

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I know about it, I’ve seen videos of it, but I have no idea how it works, or why it’s important. I mainly don’t get why it’s become to infamous.

In: Mathematics

It’s a “game” that takes place on an infinite 2D grid of cells, where the state of the game (which cells are live and which are dead) evolves at each step according to a simple set of rules.

The rules are pretty simple, you can read [Wikipedia](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) for the rules and how it works.

The significance of it is that it’s [Turing complete](https://en.wikipedia.org/wiki/Turing_completeness) (it’s a model of computation that can compute anything a Turing machine can), meaning it can simulate a computer.

the significance is it showed that very simple rules that create very advanced emergent behaviors. This has implications for all sorts of fields, but especially when discussing things like early life, and biological processes.

All sorts of very advanced including some self replicating patterns can form despite the fact the rules are very basic.

The primary significance of the “game” is that very simple rules can create systems of breathtaking complexity. The game only has four basic rules, and yet you can create oscillators, glider guns, and even ultimately a general purpose computer. If so few rules can create a computer, what is possible with the few laws of physics that the particles and waves of our universe obey?

>no idea how it works

Conway’s Game of Life is deceptively simple. Given an infinite two-dimensional grid of cells, each of which can either be [dead/empty/unpopulated] or [alive/full/populated], the game obeys the following four rules (neighbor means any of the eight surrounding cells):

1. Any live cell with fewer than two live neighbors dies, as if by underpopulation.
2. Any live cell with two or three live neighbors lives on to the next generation.
3. Any live cell with more than three live neighbors dies, as if by overpopulation.
4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.

These rules are applied to every cell on the board at once; each iteration is usually called a *tick.*

That’s it; that’s the Game of Life. Set up your board, apply the rules, and watch what unfolds.

>why it’s important

Taken from [its Wikipedia article](https://en.wikipedia.org/wiki/Conway’s_Game_of_Life):
> Since its publication, the Game of Life has attracted much interest because of the surprising ways in which the patterns can evolve. It provides an example of emergence and self-organization. A version of Life that incorporates random fluctuations has been used in physics to study phase transitions and nonequilibrium dynamics. The game can also serve as a didactic analogy, used to convey the somewhat counter-intuitive notion that design and organization can spontaneously emerge in the absence of a designer. For example, philosopher Daniel Dennett has used the analogy of the Game of Life “universe” extensively to illustrate the possible evolution of complex philosophical constructs, such as consciousness and free will, from the relatively simple set of deterministic physical laws which might govern our universe.

The game of life is essentially a grid of black or white squares that can flip colors. They flip colors based on the colors of their neighbor squares. The four rules that determine if a square should change color sort of, kind of, reminds of how living beings would interact with close living organisms. Like if you have too few neighbors you cant repopulate and will die, so a black square with too few black neighbors will “die” and turn white.

Depending on how the starting squares a colored these four simple rules can give all sorts of kind of “organic” looking results. I think it’s fair to say that it’s not so much important as it is a fascinating example of how simple rules can give very varying and complex results.

It basically shows that in a closed system, the initial starting conditions will produce the same results every time.

If our universe is a closed system, then Determinism is true and free will is a lie.

“Emergence” is the concept which states that **a complex system can arise from small simple interactions**. In other words, a bunch of little simple things that interact with each other can result in an enormously complex thing. *The collection of a things can have properties not present in any of the individual things.* The implications are vast.

For example:

* Individual ants are mega-dumb, each behaving under very simple rules. However, a colony of ants is collectively intelligent and able to solve complex problems.
* Water molecules are individually quite simple compared to other molecules, yet water as a whole is one of the most OP, broken, exploitable things in nature. Who would look at a water molecule and predict that freezing a bunch of them would produce intricate snowflakes?
* The human conscience is a result of electrical impulses getting bounced around by really basic brain cells. Modern AI is a result of many *many* simple multiplication tables that collectively find, store and reproduce complex patterns.

Conway’s Game of Life is like the most obvious illustration of this concept. Dude came up with it over 50 years ago and we are still discovering new things about it. [People have made a Game of Life pattern that makes a Game of Life pattern!](https://www.youtube.com/watch?v=xP5-iIeKXE8) So when someone wants to explain the concept of emergence, they can just point to this one game with only 4 simple rules.

there is a game. it looks a lot like checkers or othello. there are only 4 rules and no players.

when you run the four rules the board changes to a new state. run the 4 rules, new state, run the 4 rules, new state. repeat over and over and over.

now when we watch those 4 rules being run over and over we suddenly find a whole bunch of things happening that the 4 rules don’t imply should happen.

it’s the stuff that happens we find amazing. like for example, you can make a “computer” that can play playstation or xbox games in a big enough version of CGOL

to quote the games creator talking about its significance https://youtu.be/R9Plq-D1gEk&t=418
“From my point of view, it wasnt real mathematics. It was flattering to have so many readers interested in it and so on, but I personally did not think that much of it.”

and later on “Its finshed. … Nothing that followed on it was just as interesting as the basic fact that this basic rules did exist. fairly simple, and has these astonishing properties, which wherent astonishing to me.”

In other words, no significance, its just an interesting set of rules that can do astonishing things.

I’ll spell it out real simple:

Conways game of life is a simple universe simulation. One we can perform in our universe.

It is 2d, matter either exists or not and time is atomic. There are some rules that govern the matter appearing or disappearing. That’s it.

And what you see when you start spamming random cells to ON is that stable structured can exist. Moving structures too. Patterns that self replicate. It becomes Turing complete like Minecraft red stone. You can build a computer in Conways GOL.

Which means if the GOL is big enough and you shake it enough some THING could conceivably appear. A self replicating pattern that grows and makes new patterns. Maybe randomly modified itself. It would be HUGE and take FOREVER but it would be like a simple bacterium from our world.

Conways game of life shows the possibility that the simple building blocks of physics rules *could* mean that abiogenesis was possible in our universe and happened.

It also posits that our universe could be a simulation in some other higher dimensional universe.