### Turtles All the Way Up

If you’re the sort of person who reads this blog, there’s a good chance you’re already familiar with John Conway‘s Game of Life. In case you’re not, here’s the executive summary:

Start with an infinite checkerboard. Color some squares black and others white. From here on, the game plays itself. Any white square with exactly two or three white neighbors stays white. All other white squares turn black. Any black square with exactly three white neighbors turns white. All other black cells stay black. Repeat.

The goal is to choose an initial coloring that yields interesting behavior, like a snail that crawls across the page.

But here’s the coolest one ever — the Game of Life plays the Game of Life:

In case you didn’t follow that, the camera is zooming out until large blocks of squares look like single squares, each of them apparently (though not really) either solid white or solid black. The big squares obey the rules of the game, even though all the behavior is controlled by the little tiny squares, which, by the end, have become invisible. (In fact, if I understand this correctly, it takes over 35,000 generations at the little-square level to make the big squares “instantly” change color.)

The very clever people who made this possible can be found here.

A hat tip (for both the link and the title) to my friend Claudia.

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#### 7 Responses to “Turtles All the Way Up”

1. 1 1 prior probability

Cool, but I would love to see the game of life play the game of life playing the game of life

2. 2 2 Phil

Neat! Is this a general property of the Life algorithm, or only for this initial starting pattern?

3. 3 3 Steve Landsburg

Phil: It is a great accomplishment to have found an initial starting pattern that makes this happen.

4. 4 4 Jonathan Kativ

@prior probability #1: When zoomed out it looks to me like the bigsquares do exacly the same thign as the mall squares. i.e. zoom out more and wait longer and we’ll see LPLPL and (LP)^3L etc. I could be misunderstanding this but I think that we’ll see something happen on the really big scale (1 above the big scale) in (35,000)^2 moves. Can anyone confirm/deny that?

and yeah this is awesome

5. 5 5 Ken B

Oh holy crap is that cool.

In a sense I knew this was possible, because you can build Turing machines in Life, but see an actual pattern that really does it before your — or mine anyway — eyes is quite amazing.

Now to beat a drum: there ain’t nuthin here but us lifers. This shows complex behaviour but it is ALL, all of it, ALL OF IT attributable to the lowest level cells in the game playing by the fixed rules. So despite what some say, you can get very complex behavior from very simple elements.

6. 6 6 Ken B

For those interested William Poundstone wrote a terrific, approachable book on this game and realted things, The Recursive Universe.

7. 7 7 Al V.

A great example of the advances in computer processing power. In 1976, it required nearly all the resources of a DEC PDP-8 to play a 100×100 grid of Life. At the time (I was in high school) we thought that was the coolest thing ever.