Hello everybody! Today we’re gonna speak about computer science and we’re going to find out how very simples rules can sometimes generate quite complex behaviours. When I’m mentioning “complex behaviours”, I’m not speaking about you behind your screen, not at all. We’ll speak about a tiny computer simulation, which appears to be astonishing, this one is called “Langton’s ant”. Langton’s ant is a basic computer program, its principle has been imagined by Chris Langton, an American researcher. In order to simulate this Langton’s ant, we’ll need a grid where boxes can be black or white, then we imagine that someone places an ant on a box, this ant will be able to circulate among these boxes. Movement rules are extremely simple: the ant moves with respect to box color on which ‘she’ stands; if she’s on a white one, she turns right and moves on … and if she’s on a black one, she turns left and moves on as well. We add a rule: on leaving a box, its color is reversed. I repeat these rules: white box, turn to the right; black box, turn to the left and in any case, quited box’ color is reversed. Alright … then we’re gonna see what is going on by repeatingly applying these movement rules. To keep it simple, we’ll begin with a fully white grid, we put the ant on the middle. First move: the ant is on a white box then she turns to the right and the box where she stood becomes black. We do it again: on a white box, turns to the right … the color changes. White box again, turns again right and we repeat the same another time. Up to now, it wasn’t that fun but the ant comes to a black box thus she turns left. After that, white to the right,
white to the right and white, right again. OK, after 8 moves, our ant has changed a few white boxes into black ones and she went back to the center. Alright, then we can see what happens by going on applying these rules repeatingly. It’s a little tricky doing it by hand so we’ll program it. Here are the accelerated ant’s first moves … By applying these rules, you can see that … our ant is drawing pretty patterns. Very good, I stopped after 96 moves and you can see that the ant went back to the center. OK! Now that we’ve programmed it, we can continue making this ant move and see what happens even further. The ant goes ahead … one can observe that she continues drawing these pretty patterns which are pretty symmetrical … … actually it looks like some kind of flower petals. There we are, I stopped after 472 moves and we see that the ant went back again to the center. So, she drew all along symmetrical patterns … which isn’t that surprising because our rules were pretty symmetrical as well: white box turn to the right
black box turn to the left
That’s really simple But … do you think that this behaviour is going to last forever? To check this, we’ll simulate the ant very much further: we’ll go until two thousands moves. For more clarity, I’ll zoom out a little bit and then I’ll simulate this since the beginning. Are you ready? Let’s go!! We just saw that: the ant begins with symmetrical and pretty patterns … and then after these 500 moves, she seems to stop … she even seems to destroy her previous pretty patterns and nothing symmetrical appears anymore. Wierd, isn’t that? During 500 first moves, our ant made very ordered structures and she suddenly seems to have lost her order and aesthetic sense and she’s beginning to make completely disordered things. But … we didn’t change the rules during simulation at all … these have always been the same. Anyway, maybe she will finally land on her field and then if we simulate sufficiantly far, she’s gonna make … symmetrical structures again. To check this out, we’ll simulate very much further: we’ll go until ten thousands moves. I’ll zoom out again … We’ll restart and accelerate this. Let’s move on! So … regular moves first and here comes the asymmetry … the ant has obviously become a little crazy here, she’s drawing something foolish. That’s completely chaotic … This is chaotic even though it was very ordered before! That’s pretty astonishing, there has been some kind of transition. OK It goes on … We’re coming to 10 000 moves … Ooh, here’s is something happening … Surprising! You saw what just happened? Wait, I show you again slower. Suddently, quiting chaos, our ant is drawing a perfectly regular structure perfectly straight … and repeating indefinitely. This rather odd structure is called ‘the Highway’. Obviously, up to now, we can continue this simulation forever and there is nothing new coming, the ant is drawing her Highway and will bring her to infinity. So, I summarize: we have an ant moving by following really childish rules. A 4-year-old kid with pencil and paper could simulate her behaviour. During 500 first moves, we have symmetrical flowery structures, regular and ordered. Between 500 and 10 000, it’s complete chaos. After it, from 10 000 moves, a perfectly regular structure: the Highway. So what’s happened? That seems really unbelievable that such simply-ruled system can successively generate three kinds of different behaviours. Actually … nobody really knows why. You’re gonna say me that we started from a full white grid, what would have happened if we started with a grid with white but also black boxes? You can try it out and after some time, not necessarily the same time, you’ll always arrive to the Highway. Nobody has found any counterexample. We could, for instance, imagine that some configurations exist where the ant follows a periodic path, where she always lands on her field the same way … but this actually not exist. The only thing that has been demonstrated so far is that ant’s path cannot be confined. Which means that the ant goes to infinity in any way. But nobody has demonstrated that she went there by following a Highway. Besides that, some people have created Langton’s ant alternative versions for fun where there are more than two colors; even in this case, the ant produces a Highway. You perhaps want to know why serious people, such as mathematics or IT researchers have fun studying such thing. The reason is that it’s a perfect example of a system with very basic rules where very complex behaviour are observed. Indeed, this kind of situation I mean: simple rules to begin and … then complex phenomena in a global point of view; it’s something which is frequently observed in many sciences fields. For instance, in statistical physics, in order to explain how some matter structure are created … or in biology, to explain how relatively basic chemical reactions can generate such complex things as … us! By the way, Chris Langton had created her ant as being some kind of artificial life system You know, similar to Conway’s Game of Life about what I should make a video by the way. But some of such ideas: elementary simplicity
==>global complexity we find it also in human sciences such as in sociology or economics in order to try to understand group or crowd behaviours from elementary consistuents’ behaviour. All these ideas represent a new scientific study field called ‘the Emerging Science’. This Emerging Science is then something interfacing mathematics, physics, biology, computer and human sciences. And you just saw that with a simplistic system such as Langton’s ant, one cannot figure out these complex structures emergence. Then I’m not mentioning how to understand phenomena as life awakening such as we are into now Then researchers who are working on Emerging Science fields are trying to create new mathematical and conceptual tools allowing them to understand these phenomena. and … there is much to do! Thank you watching this video! If you enjoyed, don’t hesitate sharing the video to help me spreading my channel. You can find me on Facebook and Twitter. You can also support me on Tipeee if you want. Thank to all my tippers, by the way. And you can find some more content on my blog ScienceÉtonnante (in French for the moment) Thank you, see you next time!