We’re talking about Langton’s ant, which is a really interesting kind of conceptual idea that someone’s had. It’s an example of what’s called a “cellular automaton” Hello. Hello tiny dog. Oh, it’s a different person [Brady] Sorry about that interruption. Langton’s Ant is an example of what’s called a “cellular automaton”. So it’s a bit like “Game of Life”. Um… So you’ve got a grid of squares, the squares change colour depending on what’s going on in the thing. In the Game of Life, it’s slightly different because the whole thing has a set of rules, and everything changes at the same time. But in Langton’s Ant there is a specific, there’s an ant that lives on the grid, and it walks from square to square, and as it moves, it changes what the squares are doing. It’s an example of something which has a very simple rule, but ends up being really, really complex. So this is a grid, a grid of squares, and I guess– [Brady] Show me how you made it. Show us, give us all your secrets. Uh, okey. Well I got a paper bag, and cut one side of it, and then I printed it on to that, and it didn’t break my printer, which I was very happy about, and then I’ve laminated that so I can rub off. There’s the handles of the paper bag. It’s simple rules. Basically so you start off with a completely blank grid, that looks nothing like an ant. I’ll give it another couple of legs. There we go. So essentially what he does, every turn, is he either turns left 90° or turns right 90°, steps forward, and changes the color of the square as he leaves. What he does depends on what color the square he’s on is. So if he starts off on a white square, He will turn 90° to the right, and step forward, so now he’ll be over here, and as he leaves that square, he will change it from white to black. So that’s now a black square. Now he’s on a white square, so he will turn right again. And he’ll end up on this square facing this way, and he’ll change that square to black as well. And then he’ll keep doing that, so he’ll move, turn right from there, and then end up here facing that way. And we’ll change this one to black. And this is where it starts getting interesting because now he turns right and goes back on to that first square again. So he’s now on there, facing that way, and you can’t quite see him. If he’s on a black square, it’ll turn left. So he’ll now come off this way, and go this way, and as he leaves that square, he changes it from black back to white again. So, essentially, you can keep moving like this, as long as you like, and just continue changing what happens on the board. And if you start with a completely blank square, it’s kind of interesting, so he will start off by making quite simple patterns, and, kind of, things that look a bit symmetrical sometimes, But all, kind of, fairly simple, fairly self-contained. [♫] After a few hundred steps, he starts to just become more chaotic, and eventually what he’s doing looks completely random, and you’re thinking “Is this just going to carry on like this forever?” [♫] And when he get’s to, it’s something like 10000 steps, it’s a number just a bit more than 10000, he suddenly becomes completely regular. So he will start doing, like a column of a diagonal column of things that moves offwards. [♫] It’s like 104-step cycle that repeats and just continues moving diagonally off to a corner. He will carry on to infinity doing that. [♫] And it’s what’s called an attractor. So this diagonal column that he does is something that he will always end up doing. They tried loads of different initial states, loads of setting up the board to start with. He always ends up, eventually, getting to this weird diagonal column thing, and just carries on doing that forever. And I just love that. That’s it’s a thing that he’s drawn to do. [♫] You can start with any grid you want, so you can almost program it like a computer because you know that it will do, you know, whatever it was going to do, given the particular starting configuration. And, I think it was about 2000, someone actually discovered that you can use this to run any computer program. So you can build, kind of, computer logic gates, and that kind of thing within this system. And it is a Universal Turing Machine.