Le Jeu de la Vie — Science étonnante #49

Le Jeu de la Vie — Science étonnante #49


Hello everyone.
Today, we are going to talk about the game of life. So, no, I’m not referring to a board game
or a variant of Russian roulette, but a funny little computer program
imagined in the 70’s by the mathematician John Conway. For almost 50 years,
this game fascinates mathematicians and computer scientists, but also biologists and philosophers because it shows us
how a system evolving according to simplistic rules can cause
incredibly rich results. And in a way,
it helps us to understand better how a big pile of interacting atoms can end up being
the complex and thinking beings that we are. The game of life is played on an array of squares
we can take as big as we want And we imagine that each of these square
can host a cell, like a living cell. If the box contains one,
we color it in black, and conversely, if it is empty,
we leave it in white. Here is for example a possible configuration,
very simple, in which we have only six living cells. Now, the idea of ​​the game of life, is to evolve a population of cells,
in a turn-based way, according to rules that are fixed in advance
and who are childish. Rule # 1: One cell will survive the next turn only if it is surrounded by two or three neighbors. If you want, below two neighbors,
the cell dies of isolation and above three,
it dies of overpopulation. And rule # 2: if an empty square is surrounded
by exactly three neighbors, it becomes alive on the next turn. A cell is born there. To see what that gives,
try to apply these two evolution rules on our previous example. Here, we have a cell that only has one neighbor,
so who will die of isolation. Here, we have an empty square
who exactly has three neighbors, so there will be a birth here
and the same for there and for the three squares below. On the next turn,
we then have a new situation that is this one. And then we just have to start over
to evolve this new situation. There will be several deaths by overcrowding
and also some births. And so on,
we run it as much as we want. You see that applying the two rules
is extremely simple. And in fact, it’s called the game of life, but it’s not really a game
since there is no player. You have no decision to make,
apart from choosing the starting situation. And then, just apply the rules step by step,
without thinking. If we go back to our little example,
we have reached the following configuration. A square made of four cells. And there, well you can convince yourself
that nothing happens anymore. Neither death nor birth. The figure does not evolve anymore, it is stable. obviously,
the fact that we arrive at this stable structure is related to the choice we made
for the starting configuration. If we had taken a different configuration,
things would have been different. To explore different scenarios,
we will not continue to do that by hand. It turns out that the rules are extremely simple,
so very easy to program. And that will allow
to calculate changes much faster. There are many small applications
that we can download, but to be able to make beautiful illustrations,
I recoded the game of life in python, and for those interested,
I will put the link in the description. When John Conway
proposed the rules of the game of life in 1970, he and some fellow researchers started
to explore many starting configurations to see where it was going to lead. Well, of course,
if I start from a single cell or even two, they die immediately of isolation. So let’s take three cells aligned And this is what happens
when we make them evolve. We do not get a stable configuration,
as earlier, but an oscillating structure. It’s called “the blinker.” Starting from four cells in a row,
evolution stops, but on a new stable structure
nicknamed “the hive.” And with five cells,
we get after a few steps a new oscillating structure
consisting of four blinkers. But in fact, we do not always get
stable or oscillating structures. Sometimes some structures
end up dying completely. Like this one for example. Of course I will not run all the starting configurations What is funny to find
new stable or oscillating structures, is to start from an initial random situation to launch evolution
and see where it takes us. Among stable structures
that we can find this way here is for example “the boat,” “the bread,” and “the pond.” And among oscillating structures,
apart from the blinker, here is “the beacon” and the toad. What’s fascinating in the game of life is how simple little things can lead to complex structures for example take as starting situation the hive configuration that is stable, as I said, but just adding a small cell in a corner launch the evolution and here is what happens you now have four hives if I take a staircase like that with just 6 cells , look the structure develops…we wonder how far it will go and it ends up stopping towards a stable structure consisting of four blocks quite far apart from each other and it took sixty three generations for this I could show you a lot like that but the observation that fascinated Conway and that showed him the full potential of his little game is the evolution of this simple structure five cells, that’s it. And yet look and there in fact I’ll have to accelerate the movie, and also zoom out because it keeps going Again There you go The first amazing thing is that it took 1103 generations for the evolution to stabilize, which is really huge considering that we started from five little cells and the evolution was completely chaotic, with regular pattern, and finally we end up with a configuration without any symmetry consisting of four blinkers here and 15 stable structures eight blocks, 4 hives, a boat, a bread and a ship but that’s not the most fascinating thing.
In the middle of the simulation, something really amazing happened I do not know if you have noticed it. I’ll show you again look there, around the 70th generation this thing it’s called a glider, here are some others the glider is a structure that changes shape, but every four turns comes back to its configuration by moving one square diagonally we can see others a little later in the simulation. It is a structure that can move the presence of this little glider is quite revolutionary because it shows two things the first is that a pattern can have a growth that will be infinite in space during evolution.
There are eight glider that are emitted and they will therefore continue to infinity the second thing is that these gliders allow us to imagine a form of communication between structures and we will see that it opens many doors Since the game of life was imagined by Conway, “players” seek to discover or build interesting structures bigger and bigger, and richer and richer. To find large stable structures that are not just associations of existing structures, it is not so simple The biggest so far is that one. We call it Cthulu and it’s made up of 45 cell Regarding oscillators, many more were found, and in particular some whose oscillation period is not two, like the flashing but can be a larger number For example here is a structure called the pulsar, oscillating with a period of 3 meaning the figure is repeated every three turns Another more complicated example : take 10 cells in a row at first we have the feeling that the structure evolves without any particular pattern but in fact it repeats every 15 turns : it is an oscillator of period 15, called the pentadecathlon We now know oscillators of many different periods. Here is one of the biggest : it’s an oscillator of period 177. It means the configuration is repeated every 177 turns On the glider side, we could also find other structures able to move and for example the following three called spaceships respectively the small, the medium, and the big and also very pretty structures like this one: it’s the canadian Goose. Or more symmetrical like this one called 60P5H2V0. Yeah. We can imagine even pushing further but the structure that caused a little revolution in the game of life is this one : it’s called “the glider gun” And you see why : It’s a structure that oscillates while producing gliders it was discovered by Bill Gosper and bears his name: the Gosper gliding gun. And this structure solves a question that Conway had asked from the start. It shows that the number of living cells can grow to infinity with time. We have gliders who are issued with a steady pace and who never disappear. And obviously we can play trying to build guns for other types of moving structures. Here is an extreme example: remember the 60P5H2V0 ship? Well, we can make a gun for it : it’s just slightly bigger than the glider gun. In fact yes, it is really, really bigger. Look at this harmonious ballet. Don’t you find that beautiful? In fact, what is beautiful is that all this fascinating complexity stems from only two completely basic rules. Do you want more structures? this is called a smoker : it’s a moving structure, like a ship, but producing waste that remain behind it And starting from this same smoker, but by adding in his wake spaceships that will follow him, we can make an “ecological” version of it Look: the ships will convert the smoker’s debris into gliders. Here’s another pretty awesome smoking structure that’s called an online smoker. So it leaves a hell of a mess behind Earlier we saw that the glider gun was a compact enough structure that allowed to produce infinitely many cells. but in fact we can do even simpler than that. Here is a starting structure with only ten cells, that does not look like much. but let’s see how it evolves. Look: after a while we notice a kind of road paved with blocks, that builds like that indefinitely With only ten cells at the start we can show that it is the smallest possible structure with infinite growth. We can also have fun looking for structures with infinite growth, that are as fast as possible and the record is held by this structure called Max and you see why When it evolves, well it fills the space with a pattern of zebra stripes that is locally stable Well, stable, but not very robust. Look what happens if I artificially add a small disturbance when we get to the edge: Well, it’s the apocalypse. But the most spectacular structure for me is this: it’s called Breeder One It is made of ten large vessels that leave debris and eject gliders. But look what it produces: gliders and debris eventually come together to form glider guns that line up in its wake and when time passes, the number of simultaneously emmited glider increases. It’s beautiful, isn’t it? Well, it’s been a few minutes that we make pretty drawings. But you might wonder what is the use of this So if all that leaves you cold, remember that what makes the beauty of the thing is that all this complexity is generated from just two extremely simple rules, about the survival and birth of cells and that’s what makes the game of life so interesting: the fact that basic rules can give rise to extremely complex structures and behaviors. And besides, nobody could have anticipated, just but by looking at the two rules, that they could give birth to all that. And it’s this phenomenon we call “emergence” : the fact that complex structures can have macroscopic properties that can not be found in their basic constituents. These emerging situations are found in both physics and biology but also in sociology or economics when we study the behavior of groups. And that’s because it tells us about these phenomena of emergence that we are very interested in the study of simple systems easily simulated by computer, like the game of life For those who remember, I had already mentioned these issues in a previous video about of the Langton’s Ant. In the case of the game of life, we could push the investigation far enough, for example, it has been shown that there are structures capable of self-replication, like what happens with living cells and from a theoretical point of view, it has been shown that one could realize a Turing machine with the game of life. So a Turing machine is a kind of abstraction of the computer concept. It means that everything that can be calculated with a conventional computer we can also calculate with a simulation of the game of life. We can design logic gates, do operations, calculations and at the end reproduce with the game of life any program that could have been run on a computer. And here is the craziest illustration of this idea. What you see here is a series of little gliders that move in a sort of square structure that creates them. And when you look at it from a distance, these gliders filling the square is a bit like a pixel, a box that would be black. There is also a version without gliders that suddenly looks a lot like a white square And we can associate several structures of this kind to form a network of giant white or black squares And by putting the right interactions, these giant squares can evolve according to the rules of the game of life. So, I admit that this simulation was too complicated, it’s not me who made it. So we have a configuration of the game of life that can simulate a game of life: I hope that the depth of this result fascinates you as much as me. So, a question that can be asked when we have seen all this is why use those two rules and not others? And well Conway found them by trial and error trying to have rules that are both sufficiently simple, avoiding the explosion of the number of cells but making it possible to form sufficiently complex structures. There are some variations of the game of life with different rules producing also quite rich results but to try to understand what is happening, something you can do is to study an even simpler system it’s called elementary cellular automata So little vocabulary: I did not want to bore you from the start with scholarly words but the game of life is part of the class that’s called the cellular automata it concerns all systems consisting of simple elementary structures, the cells and evolving discontinuously over time according to fixed deterministic rules.
To try to make a cellular automaton even simpler than the game of life well we can try to go down a dimension and no longer consider a grid of cells but simply a line if our system is a simple line of black and white squares well it will be necessary to specify the rules of evolution according to the colors of the cells and their neighbors for example here is a possible rule of evolution There are eight possible cases to consider depending on the color of the cell and its two neighbors for example this rule tells us that if a cell is white and its two neighbors are white and well it will remain so but that in all other cases it becomes black the next turn or it stays black so let’s try to see what happens if we simulate this example from a very simple starting configuration just a black square For clarity, I will represent the evolution over time by stacking the lines. Here is the initial situation Then the next, we applied the rules, the one after and so on and if I represent that by zooming out and in an accelerated way, that’s what we get Now let’s make a small modification to the previous rule. Now: an isolated black cell dies. and here is the image of the evolution that we get And if I make another possible modification well I have another evolution To completely specify a rule of evolution, there are eight cases to consider, and since every time the result can be white or black you can convince yourself that there are only 2 power 8, ie 256 possible evolution rules in this cellular automaton So it’s quite easy to program them all and to look in an exhaustive way what happens for each of them especially as some rules are more symmetrical to each other. In the 80’s, physicist Stephen Wolfram began to study systematically all these rules and to give them a numbering to be able to distinguish them. The first rule we saw is what he calls the rule 254 the second is the 250 and the third we saw was the number 50 Let’s now look at a new interesting rule: it’s the 126. It’s again very simple: an isolated white square will stay white, a black square surrounded by two black squares dies of overpopulation, and in all other cases the box becomes or remains black and here is the evolution of this rule you may recognize this figure it’s called the Sierpiński triangle, which is it’s a well-known example of fractal structure it’s funny : we have basic rules which are completely local and that allows to create a global structure as if it had been planned in advance let’s see another example is rule number 30 and here is his evolution it’s weird : on one side we seem to have relatively regular structures and on the other it seems totally random we see from time to time larger structures but no pattern that is repeated Stephen wolfram was able to show that this structure was chaotic in a well-defined mathematical sense and that it can even be used as random number generator. Now one last example but one that has the most fascinated Wolfram : this is the famous rule number 110 and it differs from the rule 126, Sierpinski triangle, by only one change : here it is if we study its evolution then we realize that on one side on the right, it stays completely white but on the left, funny things happen at first glance the pattern looks regular everywhere but when you take a closer look we see that structures appear, spread, disappear. It seems there are interactions between these structures on a background which remains regular Structures that spread behave a lot like the gliders of the game of life and we can simulate as far as we want, this strange behavior remains it’s not something regular nor is it something chaotic it’s between the two it is as if we had just created a small world in which forms of artificial life would develop and interact as a kind of mini game of life in 2002 mathematician Matthew Cook published a demonstration of the universality of rule 110 : that is to say that can be used to simulate a turing machine, and any function computable by a conventional computer It i’s like the game of life. But despite this demonstration as for the game of life we ​​can not say we really understand why rule number 110 works like this and not the other ones. The emergence of complexity and universality of such a simple system remain an open question It shows that even the most basic computer programs have not finished surprising us

100 thoughts on “Le Jeu de la Vie — Science étonnante #49”

  1. Pour faire mumuse avec le "jeu de la vie" en vrai :
    https://www.mayotomata.com/mayotomata/engine/5c2630d204bfe929587712a1/?pluginmask=67&scale=8&autorun&speed=80

    Les cases orangées montrent la trace du précédent état

  2. Pour revenir à la vidéo "#48" ,ne serait-t-il pas possible qu'une "structure" du jeu de la vie puisse non seulement
    naitre, grandire, se reproduire et mourir (peut-être manger)?
    Et pourquoi pas Dans un hypotétique automate cellulaire dont les cellules posséderait plus de 2 états
    pourait avoid les même critères que la "forme de vie" précédement d'écrire (car oui ce serait ça)
    avec en plus la possibilité de pensser (plutôt réagir) en fonction d'informations que celle si persevrait par
    un x ou y moyen?

  3. 13:00 A ce moment précis de la vidéo, j'ai eu une grande sensation de fascination et de satisfaction d'avoir compris l'énormité du Jeu de la Vie. Cet "inception" du jeu de la vie qui crée un jeu de la vie est vraiment troublante !

  4. Et donc Dieu aurait créé quelques règles de base (jadis), et le résultat lui aurait totalement échappé…

  5. Salut !
    Intéressante cette vidéo ! Pourtant un truc me chiffonne. C'est le jeu de la vie donc censé simuler l'apparition de a vie dans le cosmos (histoire de ne pas se limiter à la planète Terre). Pourtant pour ce jeu, il a fallu un concepteur qui a réfléchit au règles de base puis les a programmés dans un système pouvant les recevoir (ordinateur). Ensuite, pour que ça fonctionne, il faut y placer au moins trois cellules car vu les règles, la génération spontanée n'existe pas et à moins de 3 cellules elles meurent…du coup, jeu de la création ?

  6. Bonsoir (de Belgique !). Merci bcp pour cette explication qui m'a passionnée… Mais très rapidement, je me suis posé la question suivantes : y a-t-il un équivalent tridimensionnelle (je suis microbiologiste, personne n'est parfait !) ? Merci pour le suivi que tu (vous) accorderas(ez) à ma question. Bien à vous,

  7. Réellement une des vidéos de yt qui m'a le plus fasciné. Je peux pas m'empêcher d'y revenir de temps en temps, je trouve vraiment ça impressionnant

  8. Fantastique !
    on avait programmé le jeu de la vie en 1980 sur un Apple 2 (au collège saint-joseph à reims, avec 2 potes de terminale qui se reconnaîtront) , pour nous amuser et nous entraîner à la programmation… c'était d'ailleurs mon premier programme en assembleur… on avait rajouté du son en faisant 1 'clic' pour une cellule qui naissait et 2 'clics' pour une cellule qui mourait… Ce 'jeu' nous fascinait déjà mais je ne savais pas à l'époque toute la richesse que ce 'jeu' comportait ! merci de m'en faire profiter 40 ans plus tard 🙂
    Ta chaîne est géniale, continue et merci beaucoup

  9. 1:45 qlqch ki va pas; la cellule a coté d la cellule du desssus doit elle aussi (prendre vie) comme elle est entourée d 3 cellules vives!!!!!!! C koi l truk

  10. Si ça se trouve il y a un énorme ordinateur géant dans une dimension supérieure à la nôtre qui simule notre monde !!! 😉 Et merde on est dans la matrice

  11. Antoine Mondoloni

    Pour donner naissance au jeu de la vie, il a bien fallu une intelligence pour en inventer les règles, n'est-ce pas ?

  12. Super video! Merci bien, j’aime rester étonné chaque fois avec tes vidéos et, en plus, ça m’aide à apprendre le français. À la prochaine alors!

  13. Trop fort. Tu m´en a encore bouché un coin l´ami. Toujours cette didactique parfaite, le même flot dans la parole, la même clarté dans l'énoncé du problème, toujours cette même pédagogie à l'épreuve des balles, ce choix des exemples qui parlent d'eux même. C´est court mais c´est toujours avec le même plaisir que je ´´bois“ tes paroles. Une fois de +, j´irai dormir un tout petit peu moins con que la veille. Je n'avais, pour ma part, jamais entendu parler du jeux de la vie. Une question toute bète: pourquoi avoir appelé ce jeux le ´´jeux de la vie“. Comme j´imagine que l´auteur est Anglo-saxon, le titre original doit être ´´the game of life“? Au moment où il invente le jeux, c´est a ce moment là qu´il le baptise ou une fois certains résultats exploités? Dans les années 70, le graphisme n´était pas ce qu´il est aujourd´hui. Ça passait bien sur les écrans de l´époque où la GUI n´était pas encore au point? Encore merci.

  14. Salut tout le monde, allez voir ma chaine , j'y expose des concepts mathematiques et des vulgarisations de façon inedite et fun.

  15. En regardant la vidéo, je me demandais si le jeu de la vie ne sera pas exploitable un jour pour créer de la matière vivante… Peut être pas le jeu de la vie lui même mais tout ce qu'il y a derrière son apparente "simplicité". Quand on voit certaines figures…
    Après tout, j'imagine que tout ça doit fonctionner à partir de fonctions mathématiques
    Vidéo super intéressante en tout cas

  16. Vantaie et fourmis

    Si on met une cellule separée de
    quatre coins comme ceci:
    ◼◼◻◼◼
    ◼◻◻◻◼
    ◻◻◼◻◻
    ◼◻◻◻◼
    ◼◼◻◼◼
    au milieu d'un quasar(le quasar doit être dans une certaine position) il se separe en quatre pulsars!

    Et si on met un clignotant au millieu d'une étoile(elle doit certainement être dans une certaine position et le clignotant aussi)elle se transforme en pulsar.

  17. J'y crois! tout est possible tout est imaginable c'est le jeu de la vie… Ah non désolé ça c'est Chevalier et Laspales

  18. avec une dimension supplementaire ça donne quoi? le jeu de la vie de base est a 2 dimension. ça serait interressant de voir l'évolution avec 3 dimensions

  19. Quand j'étais jeune je jouais à un jeu sur le jeu de la vie, des cellules rouges, des cellules bleus, la cellule qui se créée est de la couleur qui possède le plus de voisin de sa couleur (2 ou 3 quoi), à chaque tour on créé (ou en transforme je ne sais plus) une cellule de sa couleur et on voit comment ça évolue, le but étant d'éliminer toutes les cellules adverses. Qui m'aide à retrouver ce jeu ?

  20. Impressionnant, merci pour tes vidéos que je dévore!!

    Attention pour la figure que tu apprecies, je compte 10 gros vaisseaux et pas 9 ? Autour de 10:30
    Bien à toi 😌

  21. Et on parle deS accidentS à la centrâle de saint laurent des eaux; fusion de 50 kilo puis 20 kilo d'uranium enrichie dans le coeur de la centrâle et des rejet de plutonium radioactif dans les cours d'eaux pendant 5 ans et bien supérieur à ce qu'avait annoncé la centrâle avec ses eaux de rinçage?

  22. Un de mes oncles à travailler pour des centrales nucléaires, il fabriquait les cuves, et les emissions radioactive endommageait celle ci entre la fente de la cuve et le "pillier centrâle"(c'est pas le bon terme): l'écart de la fente avec la deuxieme structure était devenu tellemment importante avec le temps que l'ingenieur de la centrâle calait la fente avec sa chaussure, c'est pas une blague, lorsque les ingenieur s'approchaient avec leurs conteur, celui ci s'affolait tellemment les emissions étaient importantes.

  23. David Vander Elst

    a 9:25 pourquoi les points devant le fumeur ne bougent pas? Pourquoi se déplacent-ils donc? J'ai pas compris un truc

  24. Le problème c'est que la vie elle tourne sur 1000 règles pour des milliers de cellules dans des milliers de cases…

  25. Alors la ……..
    Mais il me semble que dans toutes les simulations il y a un attracteur qui apparait !!!Ce serait bien si tu en parlais, sans rentrer dans un doctorat en math ….

  26. Wow, j'ai rarement été aussi fasciné !!! Et le jeu de la vie qui se recrée lui même à 12:45 ça fait vraiment réfléchir

  27. Lovecraft avait raison chtullu va ts ns butter. CRAIGNEZ la colère du Dieu sous la mer. Il ne faut pas le reveiller😅😂😂😂😂

  28. Super intéressant, mais cela me laisse spéculatif.
    J'ai pu voir sur internet des versions 3D du Jeu de la vie. Si tu en as connaissance, peux tu me dire s'il existe des modèles 3D qui puisse donner des "blocs", des "unités" stables dans le temps qui puisse faire analogie à l'apparition de la vie sur Terre ?
    Merci d'avance !

  29. Petite question:
    Les étapes peuvent également être analysées en sens inverse, auquel cas on peut réfléchir dans l'autre sens:
    On cherche une structure que l'ont veut atteindre, (oscillante ou non), et on fait les étapes inverses pour obtenir toutes les structures qui finiront par aboutir tôt ou tard à cette structure recherchée, on comprend mieux que c'est chaque structure qui donne la suivante, et non la première qui par magie donne la dernière, je pense être loin d'exprimer correctement ce que je veux dire…

  30. Bonjour. Est il possible d'utiliser une autre structure que les carrés ? En utilisant par exemple comme figure de base, un pentagone régulier. Qui fait référence au chiffre d'or.

  31. Bonjour, j'ai développé un site qui permet de jouer au jeu de la vie, mais aussi de pouvoir enregistrer ses populations en base de donnée, de les publier … Bref tous les fonctionnalités d'un réseau social. Si ça intéresse quelqu'un: https://jeu-de-la-vie.mondoloni-dev.fr

  32. Science étonnante, tu n'as pas la même prestance visuelle et auditive que certains, mais pour ce qui est du contenu franchement c'est magnifique, tes sujets et ton travail pour les expliquer me régale.

  33. 15:00 On ne devrait pas avoir rien du tout si une cellule isolée meurt ? Puisque c'est le cas dans la configuration d'origine.

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