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?
+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!!
+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.
+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.
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
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.
+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.
+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.
***** 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.
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 ;)
+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
+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.
+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.
***** 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.
+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.
+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.
+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.
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.
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.
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
+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
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
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!
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...
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.
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.
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.
+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.
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
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
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).
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
@@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?
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.
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.
+MichaelKingsfordGray Depends how big the torus is. For one sufficiently large, it will just keep making highways and running into itself. Sometimes, it will run along a highway, changing one of the edges a little bit.
+Robin Powell Well I know highways still occur in many 3D implementations. Also slightly different rule-sets can create highways that fan-out with increasing area, rather than shoot out in a straight line.
A triangular grid would be interesting. There are only 3 neighboring cells: left, right, and the one you came from, so it kind of lends itself to Langdon's Ant.
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.
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).
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.
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
She says it will go off to form that highway no matter the startup position of the board. But if you start with any given start, there is a specific point it starts to take off. If you made a block black there, it wouldnt find the stable pattern at all. Is it guaranteed to keep creating the pattern that allows this highway to form? Because you could keep adding in black blocks on the right side to prevent it from spiraling off.
That blows the mind. What happens when one highway intersects with one in its path? Is there any configuration that would make a highway reverse direction by 180 degrees? Any way to predict the direction a highway will go? Does this mean that changing the rule in some way would eventually lead to some different and possibly possibly unique attractor?
+Greg Scott The first question about intersecting highways suggests we should be considering two hypothetical ants meeting and altering the colour of each others' squares, which kind of corresponds to ants in real life laying down pheromones to communicate with each other. Maybe that could make each change the direction of their highways. If a direction change was 180 degrees it could be because one of them was heading home again leaving the other to do the foraging.
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.
My daughter says, "Can we watch another one? Numberphile is really weird. It talks about deep things and gives me a sort of cold feeling in my stomach." A cold feeling? "Yeah."
i tried out the simulation with a extra feature: i randomly placed few blacks to the otherwise white space. i noticed that sometimes the ant makes huge structures, which it then removes completely! cool!
We are all ants. Born out of a random family, growing out of a random neighborhood, graduating out of a random school, we all become who we really are, doing the same things over and over again...
Is it imaginable that you can make a pattern that prevents the sub-pattern that starts the repeating pattern, or is it proven that the ant will always end up repeating this pattern after sufficient time?
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.
this really reminds me of the book "The Selfish Gene", in it Richard Dawkins puts forth as to how the pool of chemicals finally ended up having one molecule that can self-replicate: voila! the very first step to complex life.
It seems to me the way, probably the only way to avoid following the path of the "attractor" is to find another steady state for it to fall into. It's hard to imagine there's only one.
I built a program to do this. Just before the highway, it hit the edge of the screen, thus resetting it to the center. It then formed the highway going down left instead. It reset again, and deconstructed the highway!
The highway reminds me of 4 having four letters, and how all numbers when counting the number of letters they had and repeating, would eventually lead to 4.
![Wiz Khalifa - Khalifa's Home [Official Music Video]](http://i.ytimg.com/vi/wnrLCTe0Nz4/mqdefault.jpg)
Wow, Brady. Fair play on animating this by hand. Two massive thumbs up from me. Great video!
hello, old Artifexian! ☺️
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?
+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!!
Yes, in the end all civilization go extinct
+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.
+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.
+Cynix CSGO Let's traven to another universe then ¯\_(ツ)_/¯
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
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.
little did you know, you were looking at the bug the whole time
+kevnar you think i can do this with simple and plain c programming?
+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.
+kevnar if you have a simulator I would like to try it XD
Can confirm my very constructive comments are still being blocked by Numberphile.
wait what if we played langton's ant and the game of life on the same grid at the same time?
+icecreamget nice thinking!!!
+icecreamget - Life would eventually evolve into an anteater.
+RFC3514 accidentally did more drugs and your post vibrates with my soul now lol
fortnite
War
I really liked the music in this one😀
Q: Why don't ant-eaters ever get sick?
A: Because they're full of anti-bodies!
Dad humour FTW
+AlanKey86 if it was not your music in the video, I'd be having harsh words right now! :)
+Numberphile who doesn't love Alan
+AlanKey86 Personally I found the punch line to be anti-climactic.
+AlanKey86
Gurl: "Dad! Make me a sandwich, pls."
Dad: "Abrakadabra! You're now a sandwich!"
Gurl: *crys*
Dad humour ftw
+AlanKey86 wouldn't those be ant-y bodies?
whoever edited this: THANK YOU VERY MUCH FOR THE EFFORT!!!
LOL This is exactly what 'ants' do in Powder Game!
Yes, I think they work on Langton's Ant's rules.
+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.
***** 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.
+Bazzabazeman oh memories...
I thought it was called Dust
you did this in photoshop? Isn't there a better way in programming this?
Yeah they can just use BleuJ for the board and the logic is simple enough to program.
you can also kinda program photoshop to do actions, which are kinda like macros
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 ;)
+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
+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.
+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.
***** 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.
+Michał Dzięgielewski Simplified? Langton's ant has two damn rules.
Universal Turing Machine with just 2 bloody rules?! Wow
+666Tomato666 I know, right, amazing
+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.
+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.
+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.
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.
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.
"if two ants are on the same square, neither of them change direction" or something like that
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".
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
Truly enlightening. Thank you.
A way cooler name would be "The Stairway to Heaven". From the caos we ascend
*chaos
I wrote a Langton's Ant screensaver back in the 90's, it was a big hit with the geeks in the office.
Love this. One of the coolest Numberphile videos i've seen in a while :)
video does this phenomena justice. speech, editing, music. thanks for the goosebumps.
Very cool! Must've taken quite a while to animate this one.
+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
+floatboth auto mouse programs ;)
+dashn64 Photoshop macro
omg he actually made all of that simulation by hand
i thought he wrote a simulation
WAIT A SECOND HALFWAY THROUGH THIS I REALIZED THAT IN POWDERGAME FROM DANBALL THERE'S AN ANT MATERIAL THAT SEEMS LIKE IT DOES THIS
Maybe one of the most poetic videos you've uploaded
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
Damnnn Brady, you animated that by hand. Man take a bow.
Antman movie trailer?
+asre wefwefw That would make the movie very exciting
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!
+George Andrei Gogan seems that the timing has to be perfect: the second time i tried this, it just started building 2 highways.
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...
Great video and props to whoever had to edit every frame...
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.
I can't concentrate. Audrey made my mind melt from cuteness.
You drew everything of it on photoshop? Amazing impractical work.
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.
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.
Please stop separating a video into two parts :/
+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.
+Numberphile is there any chance that you could do a video on sixtysymbols about poinsot's ellipsoid and gyroscopes
+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.
+Numberphile I think what they're saying is that the extra footage should be part of the first video rather than its own video.
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
I'm in love with the music!
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
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).
I made animated gifs of this in Python using the Pillow library today while at work.
I was scrolling through some playlists of Numberphile, desperately searching for one that I hadn't already watched, and 'twas this one!
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.
Never really appreciated it before, but the music played during the ant sequences is beautiful!
That reminds me a lot of the Syracuse sequence. Very cool.
M I N E C R A F T
Yessir
Logdotzip
Really useful tool for understanding attractors in general
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
Can you prove it always does this cycle?
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?
@@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?
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.
+draco18s And if you let it keep going that way it way it will eventually return to the area from which the highway started.
Excellent background music...!
Totally going to compute this!
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.
Do a video about Langton's uncle
What happens if you put it on a triangular grid? Would it behave in the same way?
Or hexagonal?
+MichaelKingsfordGray Depends how big the torus is. For one sufficiently large, it will just keep making highways and running into itself. Sometimes, it will run along a highway, changing one of the edges a little bit.
+Robin Powell Well I know highways still occur in many 3D implementations. Also slightly different rule-sets can create highways that fan-out with increasing area, rather than shoot out in a straight line.
A triangular grid would be interesting. There are only 3 neighboring cells: left, right, and the one you came from, so it kind of lends itself to Langdon's Ant.
Yes. Eventually
And now I will remember Audrey every time I see an ant.
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.
From an argument regarding the state of human consciousness to an ant doing his own thing to infinity. Interesting subject shift.
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).
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.
That is simply amazing
I had a hard time getting over her snubbing the tiny happy dog.
Very interesting! Thanks numberphile!
0:08 - Attack of the Killer Audrey was the best part of this video. "Hello, tiny dog! 'It's a different person!' "
Audrey is love, Audrey is life.
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
Yay! We need more videos on cellular automata
+1 for the Audrey cameo
She says it will go off to form that highway no matter the startup position of the board.
But if you start with any given start, there is a specific point it starts to take off.
If you made a block black there, it wouldnt find the stable pattern at all.
Is it guaranteed to keep creating the pattern that allows this highway to form?
Because you could keep adding in black blocks on the right side to prevent it from spiraling off.
it starts erasing itself when given a boundary
Also appears in the "powder game".
That blows the mind. What happens when one highway intersects with one in its path? Is there any configuration that would make a highway reverse direction by 180 degrees? Any way to predict the direction a highway will go? Does this mean that changing the rule in some way would eventually lead to some different and possibly possibly unique attractor?
+Greg Scott The first question about intersecting highways suggests we should be considering two hypothetical ants meeting and altering the colour of each others' squares, which kind of corresponds to ants in real life laying down pheromones to communicate with each other. Maybe that could make each change the direction of their highways. If a direction change was 180 degrees it could be because one of them was heading home again leaving the other to do the foraging.
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.
My daughter says, "Can we watch another one? Numberphile is really weird. It talks about deep things and gives me a sort of cold feeling in my stomach." A cold feeling? "Yeah."
was this the animation you were talking about on twitter? because I appreciated it.
1:15 unsolved rubik's cube on the upper right! Brady, can you solve a rubik's cube?
i tried out the simulation with a extra feature: i randomly placed few blacks to the otherwise white space. i noticed that sometimes the ant makes huge structures, which it then removes completely! cool!
Now that's a nice drawing of an ant.
Nice video btw.
that must of have been fun to edit
We are all ants. Born out of a random family, growing out of a random neighborhood, graduating out of a random school, we all become who we really are, doing the same things over and over again...
Now that's something very interesting. I love that
0:15 do not apologize i love that dog it is so cute
LOL after 10000 steps! I would not have expected that
Is it imaginable that you can make a pattern that prevents the sub-pattern that starts the repeating pattern, or is it proven that the ant will always end up repeating this pattern after sufficient time?
Open problem
Things can really get interesting when you bring in two ants with certain starting configurations.
Its a great example to show how random things become quite ordered ... life might have also resulted from such ordered ness in randomness.
+Ashwin Kumar k It's not random becoming order, it's order creating the illusion of random.
The editing!! haha nice video!
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.
Im going to write this program right now ! Awe inducing stuff :O
This is brilliant!
this really reminds me of the book "The Selfish Gene", in it Richard Dawkins puts forth as to how the pool of chemicals finally ended up having one molecule that can self-replicate: voila! the very first step to complex life.
That unsolved Rubik's cube. It hurts my eyes!
It seems to me the way, probably the only way to avoid following the path of the "attractor" is to find another steady state for it to fall into. It's hard to imagine there's only one.
This is absolutely fascinating :D
Now, make langton's ant in langton's ant. it's been done with Conway's game of life
I built a program to do this. Just before the highway, it hit the edge of the screen, thus resetting it to the center. It then formed the highway going down left instead. It reset again, and deconstructed the highway!
A beautiful ant indeed.
How interesting. oO More stuff like that!
Ooomygod I can't believe ya'll animated that in illustrator that's not how you do that lol
Thats pretty cool! This is the kind of videos I like :)
The highway reminds me of 4 having four letters, and how all numbers when counting the number of letters they had and repeating, would eventually lead to 4.
It's a nice site logic problem to test your programming skills against too.