Langton's Ant - Numberphile

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Langton's Ant - starring Katie Steckles (and Audrey).
More links & stuff in full description below ↓↓↓
Extra footage: • Langton's Ant (extra f...
The 104-steps: • Langton's Ant (the 104...
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Videos by Brady Haran
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13 сен 2015

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Комментарии : 564

@Artifexian 9 лет назад

Wow, Brady. Fair play on animating this by hand. Two massive thumbs up from me. Great video!

@myrinsk 2 года назад

hello, old Artifexian! ☺️

@timsonins 3 года назад

The emotional piano music at the end as the ant continues building his highway to infinity is just so cute and calming. It makes me feel emotions I last experienced in childhood

@EugeneKhutoryansky 9 лет назад

I wonder how many other things in life are like this, where we initially get a different chaotic pattern depending on the starting conditions, but then after enough time passes, we always end up getting the exact same outcome. For example, could the development of civilizations throughout the universe have this phenomena?

@Benpurple4 9 лет назад

+Eugene Khutoryansky Please don't say that! We can beat the cycle! Or we're the first. Or life is just really really hard to keep alive so we're spread out too far to observe each other. Or perhaps we're being observed already and one day we will ascend in to the galactic counsel. We WILL NOT PERISH!!

@Bladma12 9 лет назад

Yes, in the end all civilization go extinct

@EugeneKhutoryansky 9 лет назад

+Benpurple4, the outcome need not be negative. The outcome could be that all civilizations eventually turn into peaceful, technologically advanced, space exploring civilizations, regardless of how they started.

@thatsquidwardfeel5567 9 лет назад

+Eugene Khutoryansky The outcome absolutely needs to be negative. Even when there's a civilization that could carry on to infinity, there'll be a point erhe there's no hydrogen left in the universe and the last sun burns out.

@Brotcrunsher 9 лет назад

+Cynix CSGO Let's traven to another universe then ¯\_(ツ)_/¯

@icecreamget 9 лет назад

wait what if we played langton's ant and the game of life on the same grid at the same time?

@numberphile 9 лет назад

+icecreamget nice thinking!!!

@RFC3514 8 лет назад

+icecreamget - Life would eventually evolve into an anteater.

@icecreamget 8 лет назад

+RFC3514 accidentally did more drugs and your post vibrates with my soul now lol

@superkobster 4 года назад

fortnite

@bobspivics502 4 года назад

War

@greg.sym.4115 9 лет назад

I really liked the music in this one😀

@kevnar 9 лет назад

I made this on my computer one day. Can confirm the highway. It pissed me off. I thought the program was broken and I searched the code for bugs for like two hours.

@j7a1k1e 9 лет назад

little did you know, you were looking at the bug the whole time

@TobiDeMonkey 9 лет назад

+kevnar you think i can do this with simple and plain c programming?

@gorden2500 9 лет назад

+TobiDeMonkey don't see why not. The logic behind the ant, as you saw, is very simple. i'd guess the matter of displaying this world wold take up more then the logic it self.

@Blindboard100 9 лет назад

+kevnar if you have a simulator I would like to try it XD

@TheMrTape 9 лет назад

Can confirm my very constructive comments are still being blocked by Numberphile.

@AlanKey86 9 лет назад

Q: Why don't ant-eaters ever get sick? A: Because they're full of anti-bodies! Dad humour FTW

@numberphile 9 лет назад

+AlanKey86 if it was not your music in the video, I'd be having harsh words right now! :)

@Saxie81 9 лет назад

+Numberphile who doesn't love Alan

@mestiarcanus 9 лет назад

+AlanKey86 Personally I found the punch line to be anti-climactic.

@ellu999 9 лет назад

+AlanKey86 Gurl: "Dad! Make me a sandwich, pls." Dad: "Abrakadabra! You're now a sandwich!" Gurl: *crys* Dad humour ftw

@Kram1032 9 лет назад

+AlanKey86 wouldn't those be ant-y bodies?

@headshock1111 9 лет назад

whoever edited this: THANK YOU VERY MUCH FOR THE EFFORT!!!

@Bazzabazeman 9 лет назад

LOL This is exactly what 'ants' do in Powder Game!

@Paulwe1 9 лет назад

Yes, I think they work on Langton's Ant's rules.

@QwertyuiopThePie 9 лет назад

+Bazzabazeman Wow, didn't expect to see anyone remembering that game. Yeah, the ants are based on Langton's Ants, but with modification as to how they fall and spread elements and such things.

@QwertyuiopThePie 9 лет назад

***** Powder Game is the reason Powder Toy exists. It was basically Powder Toy before there was such a thing as Powder Toy, but when the development slowed down the PT developer basically took matters into his own hands. In a way, you could consider PT an unofficial sequel of sorts. But don't worry. It'll go the way of Powder Game eventually.

@magicandmagik 9 лет назад

+Bazzabazeman oh memories...

@Naijiri. 8 лет назад

I thought it was called Dust

@Lucas-mq2pd 4 года назад

M I N E C R A F T

@Eli20021_ 4 года назад

Yessir

@nethaura4922 4 года назад

Logdotzip

@Tapecutter59 6 лет назад

I wrote a Langton's Ant screensaver back in the 90's, it was a big hit with the geeks in the office.

@voxorox 9 лет назад

I'd like to see a simulation of what happens with 2 of them on the same grid. We'd have to add a rule about collisions (not going to the same space at the same time) but I'd like to see the outcome of that.

@o5-1-formerlycalvinlucien60 Год назад

"if two ants are on the same square, neither of them change direction" or something like that

@Graphomaner 9 лет назад

Many years ago I discovered Powder Game, cute little sanbox made in Java. There was an Ant element in there. I think it might be a simplified version of Langton's Ant behaviour coded into that. Amusing ;)

@bvlampe6801 9 лет назад

+Michał Dzięgielewski yeah, maybe... They do actually make such lines when they have an element to make it with and only stop at the border... Now I think so too, but you gave me the idea :D

@DThorn619 9 лет назад

+Michał Dzięgielewski That game as evolved so much since back then, look up something called Powder Toy, it's a way more advanced version of the original Powder Game.

@QwertyuiopThePie 9 лет назад

+Asad Mirza It was created because Powder Game didn't work on a specific distro of Linux at the time, I believe. Of course, they've both stagnated by now.

@QwertyuiopThePie 8 лет назад

***** Sounds about right, Even fewer people play the games that led to PG (doesn't help that the fallingsandgame website fell down). TPT is getting its turn in the sun, for now.

@Colopty 8 лет назад

+Michał Dzięgielewski Simplified? Langton's ant has two damn rules.

@666Tomato666 9 лет назад

Universal Turing Machine with just 2 bloody rules?! Wow

@stocktonjoans 9 лет назад

+666Tomato666 I know, right, amazing

@unvergebeneid 9 лет назад

+666Tomato666 To be fair, the intelligence so to speak is in the preparation of the initial conditions. So for such a simple thing as an infinite loop, you'll need an infinitely large grid with infinitely many logic gates already in place. So while it's fascinating, it's also a bit of cheating. It's almost like saying: "Look, I can build a Turing machine with only one rule: electrons follow an electric charge gradient!" And then you switch on your computer. With the added benefit that your CPU is finite in size.

@TimJSwan 9 лет назад

+Penny Lane Right. For any instance run, there's the complexity of the universal inference rules, grid memory layout, and starting state. Ant: (2 update + 2 move x 4 choice, 2D x 2State + x,y location, starting state) Life: (4 update x 9 check, 2D x 2State, starting state) Rule 110 (8 update x 3 check, 1D x 2State, starting state) Where update is the number of update rules, check is how many memory cells need to be checked, and 1D 2D are the number of dimensions in memory.

@CorwynGC 9 лет назад

+Penny Lane Except that the concept of a Turing machine is just a state machine on a one dimensional tape. This shows that for a 2 dimensional grid, a state machine with only two states (and two symbols) is sufficient. Turing machines aren't complicated, that is the whole point. 1-denemsional Turing machines require at least 2 states and 3 symbols. NO cheating is involved here. No Turing machines does much of anything without a program.

@unvergebeneid 9 лет назад

CorwynGC Agreed, the intelligence is in the rules again but you can recycle the rules in actual Turing machines. You can and do start with an empty tape.

@hallowstar4857 9 лет назад

Redolent to how the first proto rna likely formed, random changes to a set of molecules over million of years till one happens to have a structure that allows for it to replicate itself

@Satchboy71 9 лет назад

An example of order out of chaos? If you let the ant do its thing long enough it eventually creates the conditions for the "highway".

@huh_wtf 2 года назад

Damnnn Brady, you animated that by hand. Man take a bow.

@jall3ri 8 лет назад

I just followed the 104 step video and noticed if you start with just 15 dark squares the ant will just do the highway: Let Grid Coordinates 0,0 be where the ant starts with it white with ant facing up. start with the following cells darkened (first number column negative=left of origin positive=right, second number=row negative=above, positive=below) -2,1;-2,0;1,0;-2,-1;1,-1;-3,-2;-2,-2;-1,-2;1,-2;-3,-3;0,-3;1,-3;2,-3;-2,-4;-1,-4

@Qbone15 9 лет назад

Love this. One of the coolest Numberphile videos i've seen in a while :)

@PsychoGod9898 9 лет назад

you did this in photoshop? Isn't there a better way in programming this?

@AnthonyMata 8 лет назад

Yeah they can just use BleuJ for the board and the logic is simple enough to program.

@rokavsic 7 лет назад

you can also kinda program photoshop to do actions, which are kinda like macros

@janesarayevo608 9 лет назад

A way cooler name would be "The Stairway to Heaven". From the caos we ascend

@j.hawkins8779 3 года назад

*chaos

@cjp21211 9 лет назад

Truly enlightening. Thank you.

@TCLA248 9 лет назад

Great video and props to whoever had to edit every frame...

@clnlws44 8 лет назад

omg he actually made all of that simulation by hand i thought he wrote a simulation

@ac_nero 3 года назад

video does this phenomena justice. speech, editing, music. thanks for the goosebumps.

@Frosty-oj6hw 9 лет назад

I think this game of life is the little app that Daniel Dennett uses to help explain partly how we get complexity from simplicity, and how the sum of parts of a system can be free while the components are not free (regarding free will) a very interesting talk you can find on youtube.

@MidoriFlygon 9 лет назад

The way the ant was making the pattern immediately reminded me of the ant element from the Powder Game I used to play in high school and middle school.

@georgegogan 9 лет назад

thanks numberphile! there is a java simulation website for langton's ants. i tried something interesting: i placed an ant in the middle of the screen, then waited. after it started the highway, i placed another and in the same place as the first one. after a few minutes, a very interesting pattern shows up! enjoy!

@georgegogan 9 лет назад

+George Andrei Gogan seems that the timing has to be perfect: the second time i tried this, it just started building 2 highways.

@grapefruittango4707 7 лет назад

WAIT A SECOND HALFWAY THROUGH THIS I REALIZED THAT IN POWDERGAME FROM DANBALL THERE'S AN ANT MATERIAL THAT SEEMS LIKE IT DOES THIS

@Smittel 9 лет назад

Those simple things are absolutely amazing. Ppl be like wow i wrote this hyper complex self learning programm. I have a feeling that a real general AI would only need a few lines of code...

@JupitersDancer 9 лет назад

Maybe one of the most poetic videos you've uploaded

@Anthony-cn8ll 4 года назад

I made animated gifs of this in Python using the Pillow library today while at work.

@jonathanfraser1489 9 лет назад

Very interesting! Thanks numberphile!

@particleonazock2246 4 года назад

I was scrolling through some playlists of Numberphile, desperately searching for one that I hadn't already watched, and 'twas this one!

@johnray6906 9 лет назад

From an argument regarding the state of human consciousness to an ant doing his own thing to infinity. Interesting subject shift.

@GraniteValleyDave 9 лет назад

Very cool! Must've taken quite a while to animate this one.

@mighty8357 9 лет назад

+dashn64 I'm pretty sure this was done using some kind of algorithm and screen recorded what happened. Nobody in their right mind would do this 1 square at a time :D

@tggt00 9 лет назад

+floatboth auto mouse programs ;)

@nidky 9 лет назад

+dashn64 Photoshop macro

@BearshiMisnes 6 лет назад

And now I will remember Audrey every time I see an ant.

@NxCloudTest Год назад

There is chaos in order, yet there is order in chaos. The ant has simple movement instructions but its path turns into a highly chaotic one. However, after a certain point, it goes from chaos to repeating the same pattern again.

@agargamer6759 3 года назад

I'm in love with the music!

@asrewefwefw1105 9 лет назад

Antman movie trailer?

@UriGerhard 9 лет назад

+asre wefwefw That would make the movie very exciting

@LucidEnigma21 9 лет назад

The editing!! haha nice video!

@parouuu 8 лет назад

Now that's a nice drawing of an ant. Nice video btw.

@MazeFrame 9 лет назад

This is brilliant!

@Reydriel 9 лет назад

This is absolutely fascinating :D

@phycoman4561 9 лет назад

This reminds me of a psuedo random number generator used in a computer simulation. All psuedo random number generators eventually end up in these sort of short loops and thats when they stop being usefull, but the good ones dont start looping until like 234,643,234,534,755 iterations. It all depends on the values of the starting rules.

@Zahlenteufel1 9 лет назад

Totally going to compute this!

@draco18s 8 лет назад

It gets even *more* interesting if you make the left and right edges connect, and the top and bottom (topological torus). Eventually the ant fills the grid with alternating diagonal stripes, 2 pixels thick.

@jall3ri 8 лет назад

+draco18s And if you let it keep going that way it way it will eventually return to the area from which the highway started.

@Lightningfootjones 9 лет назад

Really interesting video!

@martinluther123 9 лет назад

Thats pretty cool! This is the kind of videos I like :)

@MichaelFrancisRay 9 лет назад

I love this.

@xapemanx 9 лет назад

That is simply amazing

@Alex_Deam 3 года назад

Maybe I'm overthinking, but the trajectory of "some kind of order -> chaos -> uniform line" reminds me of water coming out of your tap, rushing round the sink semi-randomly, and then heading all down the drain. Anyway I came here for the dog, stayed for the cellular automata.

@justgonnastay 9 лет назад

I had a hard time getting over her snubbing the tiny happy dog.

@thomassomeone4868 8 лет назад

I can't concentrate. Audrey made my mind melt from cuteness.

@knights8400 9 лет назад

Do a video about Langton's uncle

@NoriMori1992 6 лет назад

Never really appreciated it before, but the music played during the ant sequences is beautiful!

@santinossantamonica 9 лет назад

outstandingbounds!!!!

@EmmisonMike 9 лет назад

Audrey is love, Audrey is life.

@KrishnamKumawat 9 лет назад

So freaking Awesome!!!

@sachinayadav 6 лет назад

Excellent background music...!

@mathematicalmatt 9 лет назад

What is super cool is when there are multiple rules and multiple colors, like turn left on orange and change to blue, and so on. There are some pretty amazing highways that can form from multi-ruled langton's ants.

@Kilroyan 9 лет назад

How interesting. oO More stuff like that!

@becca_chan420 9 лет назад

that must of have been fun to edit

@Engeneeringtips 7 лет назад

Incredible

@GullySquad02 9 лет назад

+1 for the Audrey cameo

@krccmsitp2884 Год назад

0:39 This reminds me of John Carpenter's "The Thing".

@medievalogic 9 лет назад

Im going to write this program right now ! Awe inducing stuff :O

@janesarayevo608 9 лет назад

this one was a nice video

@missliketrains2 9 лет назад

Now that's something very interesting. I love that

@dragonslayer050819 9 лет назад

it starts erasing itself when given a boundary

@Tweakimp 9 лет назад

Please stop separating a video into two parts :/

@numberphile 9 лет назад

+Franz W this video is one part - I just also share the stuff that was cut out of this video, rather than having end its life unseen.

@hakkbak 9 лет назад

+Numberphile is there any chance that you could do a video on sixtysymbols about poinsot's ellipsoid and gyroscopes

@NoahTopper 9 лет назад

+Numberphile I always felt like this was rather obvious, but many people don't seem to get it. If there weren't multiple videos, then we wouldn't be seeing the extra footage at all.

@E1craZ4life 9 лет назад

+Numberphile I think what they're saying is that the extra footage should be part of the first video rather than its own video.

@Tweakimp 9 лет назад

DJTripleThreat78 Who doesnt have 10 more minutes to watch a video on youtube lol. you can always turn off the video by pressing alt+f4. numberphile can also just paste the extra bit on the end of the first video and say "from now on extra stuff". all in one video, still devided

@BruceRicard 8 лет назад

That reminds me a lot of the Syracuse sequence. Very cool.

@RinoaL 9 лет назад

now lets add the color grey, grey will make him go straight and then we can think of some rules for turning a block grey.

@TheCouchpotat0 9 лет назад

Yay! We need more videos on cellular automata

@hekkn 4 года назад

Now, make langton's ant in langton's ant. it's been done with Conway's game of life

@willlewis77 9 лет назад

Really useful tool for understanding attractors in general

@ericsbuds 9 лет назад

LOL after 10000 steps! I would not have expected that

@NoriMori1992 8 лет назад

0:08 - Attack of the Killer Audrey was the best part of this video. "Hello, tiny dog! 'It's a different person!' "

@HeavyboxesDIYMaster 9 лет назад

A beautiful ant indeed.

@ar_xiv 9 лет назад

Ooomygod I can't believe ya'll animated that in illustrator that's not how you do that lol

@ashwinkumark1400 9 лет назад

Its a great example to show how random things become quite ordered ... life might have also resulted from such ordered ness in randomness.

@PhilHibbs 8 лет назад

+Ashwin Kumar k It's not random becoming order, it's order creating the illusion of random.

@DanDart 8 лет назад

I was playing with golly a couple of months ago and found that if you have many ants, they don't necessarily go off on a big crazy trip like that, you can get pure cycles

@PopeLando 9 лет назад

It's official. Audrey is now invading all of Brady's other work. Prof Martyn and Phil and Tony and Ed and even James are going to have to fight for screen space alongside the chihuahua.

@volotat 9 лет назад

You drew everything of it on photoshop? Amazing impractical work.

@Lucas72928 9 лет назад

1:15 unsolved rubik's cube on the upper right! Brady, can you solve a rubik's cube?

@ShannonWare 9 лет назад

I was a big fan of _Life_ back in the day (original Macs); so I am happy to pass this sort of information on to my daughters (who all have a love-hate relationship with maths).

@lordfeish1927 4 года назад

reminds me of a sequence i found one time that looks random at first and then every term after 300 something is 97

@catdogfishdogcats 8 лет назад

we need more casual comments about the dog. He just wanted to learn about Langston's ant too.

@RoloFilms 9 лет назад

That unsolved Rubik's cube. It hurts my eyes!

@gamingcookiereal 5 лет назад

0:15 do not apologize i love that dog it is so cute

@sabaca304 9 лет назад

Every life starts in totally different chaotic starting conditions. But in the end we are all bond to die.

@Marci124 9 лет назад

Also appears in the "powder game".

@rekagotik2785 3 года назад

I remember something similar to this in the dust game in Danball

@xXxGnuVirusxXx 7 лет назад

i died at the dog part XD

@LittlePeng9 9 лет назад

As far as I know, it has not yet been shown that the ant will always create the highway. Unless I missed some news, it is only known that the ant's trajectory is unbounded.

@racheline_nya 5 лет назад

now introducing, the 3D langton's ant: the tiles can now have 6 colors. on red, yellow, green, cyan, blue and purple, the ant turns clockwise, looking from above, east, north, below, west and south respectively. at the start, everything is red

@goodlookingcorpse 3 года назад

What rule governs changing colors? Presumably it would need to be an arrangement where A -> B -> C -> D -> E -> F -> A, otherwise there'd be particular colors that could never appear (as an extreme example, if red became cyan and cyan red, this would be identical to the original).

@whoeveriam0iam14222 9 лет назад

would be interesting to see if there would be a black square somewhere on the highway.. and then see where it goes depending on where on the highway that dot would be.. and how long it would take to get back to highway-ing

@crazycanadian7223 9 лет назад

That dog is too damn cute.

@travispetit2410 8 лет назад

Can you prove it always does this cycle?

@simonenoli4418 7 лет назад

Travis Petit do you mean if the ant will continue on forever or that given specific rules the ant will always end up in a cycle?

@cptrikester2671 4 года назад

@@simonenoli4418 I would like to know the second part. If the ant / floor is given any set of simple instructions, and then started on any initial floor pattern, will it always end up in a 'highway' sequence? Can the number of steps to 'sequence repeat' be calculated?

@Imbrium66 8 лет назад

I actually found this fascinating enough that I went into excel and wrote a program that does exactly the same thing (for practice in part). Put in the number of steps and watch it go.