Langton's Ant 3D 

What interests me the most after watching this is that no matter how many dimensions there will be the Langton's ant it will always eventually end up making a highway or an infinite pattern no matter the different rules you apply to it. It's just amazing

Everybody gangsta till Langton's Ant griefs your 2b2t Minecraft base

I love how both the simulation speed and the camera zooming out scale together

Cool! I don't care that there's like a thousand more people that did this, that's just so dang satisfying:) How is this video not viral yet?

*@Andrew Vasenev* 8:52 This camera movement was great to determine the depth in this video, it would be good with a continuous movement like that around the blocks.

Langton’s Ant and other things like it have always fascinated me So, naturally I was very happy to see this video in my recommended It’s just so cool lol

The first chaotic one looks really cool

Woah! I just realized something (it might be obvious to some, but for me, this is mind-blowing): The colors on top are the ones that the ant has traveled though the most, while the lower ones are traveled through the least. Or in other words, whatever color is set to be the one that spawns when the ant hits an empty space, that color represents a space that is traveled the least and the colors following are the ones more and more traveled on by the ant until finally, the color that comes right before the first color is the one that is traveled on the most. You can see this pretty easily with 2D maps, but even on here its very apparent on the map at 11:47. Most of the outside is purple (the color the ant places when it reaches empty space), while the middle layers are mostly grey and red, and most of the blue is one the inside. I think of it kind of like this: on a map, the blue blocks would be the well-trodden highways, the greys and reds would be the towns or livable land, and the purple would be the mountain peaks. Yet another way to think of it might be to imagine the blocks as numbered 1-4 (or however many colors there are) starting from the top block in the program being 1. Then, when the ant places that first block, it will be purple with a number of 1. When the ant travels to the block a second time, it changes the block to grey with a number of 2, which means that space has been occupied twice. The same happens when the ant visits it a third time; the block changes to red with a number of 3, meaning it has been occupied by the ant tree times. And it's the same with the fourth and last block. However, after the ant reaches a space a fifth time, the block goes back to purple, meaning its been to that block five times. So here I guess is where you can say that the color represents that the ant has been through a certain space a multiple of the position of the current color. So my first statement is slightly incorrect, but for the outside layer of the map you see, it's mostly true. What follows from this is that technically, you could use an infinite amount of colors on this map to denote every single unique number of times the ant has passed through a certain space. Imagine just taking the blocks' turning information and duplicating it indefinitely below the existing programming, but assign a new color to each turn. I think the map would still end up the same shape. (Am I thinking about that correctly? I feel like I might be wrong to think that.) But regardless, a limited color map actually stores a lot more information than you might think. (Please let me know if I've made a mistake somewhere.)

The first chaotic algorithm looked like lilipads overlapping onto eachother

Cool project! Also, what's the music used in the video?

SUPER! Muchas gracias por tan buen video. Las matemáticas y su mágico lenguaje.

Imagine a Langton ant that eventually makes Rick astley.

One thing Id like to see is it always rendering tbe most recent block on top, so when its noodling around inside/behind the thing you still get a bit of a sense of what's going on.

And this, is how Minecraft terrain is made.

How did this not go viral!?!?!?!?!?

That would make some insane Minecraft art

I love these langtons ant things

Good video bro. I like your favorite. My favorite is simple but highway doesn't start for a lot of iterations. Thanks so much.

*4:19** Stairway to Heaven* :D

7:38 That one's neat! It looks like a cactus.

Considering the variety of patterns 2-D turmites can make, what patterns have you found in 3-D ones that you can't show in 2-D?

It's just beautiful!

Super cool man, thank you!

Hypothetically could a langton’s ant be created that constantly builds *new rules for itself* and thus never achieves a highway?

Can you please explain what the rules imply?

This is awesome! I also played with your Langton's Ant 3D program for a lot(like, a million steps) and was immersed at the graphic and settings you made! Thank you for the video and the application! p.s. is there any way to change the initial setting before playing? i would be even more satisfied if i could see the difference when a bit of initial colored blocks are put:)

You should decrease the opacity on all cubes except the one the ant is currently on.

1:59 ❌langton's ant ✅langton's plant

Love how you implemented this, though I do have some questions: Your program shows 4 rotations, but shouldn't it allow 6, since there are 6 possible 90-degree rotations of the cube Follow-up question, what patterns might be possible if instead of strictly only turning left or right, you included the whole group of rotations (including no rotation, turning around, or some combination of rotation around different axes)? Are there any space-filling patterns in 3 dimensions, one that can fill volumes in a regular manner rather than just planes?

I,ve already downloaded the program and when i open "Langton's Ant 3D.exe" it works but when i try to start using the buttons Start/stop or using enter it doesnt work (all the other comands work but the main ones like that one doesnt), do you know why i that happening to me?

The Langton's Ant actually appeared in a Minecraft April Fools Update!

This is fascinating. Thanks for making that video. Can we ask what t software you use?

Whenever highways form, I can't resist going "weeeeeee"

How is this implemented? Like how many directions can the ant face in? It should be 24 right? 6 directions × 4 orientations per direction

Do any algorithms build a "cage" that the and can never get out of?

Now do 4D. I'll wait.

now make 4-dimensional langton's ant

The third dimension allowed langton's ant to make 3d highways. Cool.

how can I change the speed

Very interesting.

You should do a 3d slice of 4d langstons ant

Wow!

are there any algorithms that make cubes and are besides brute-forcing, can you have an ant make a menger sponge?

but did one of them go up up down down left right left right?

Why does the ant only goto infinity in the Cartesian axes

What happens when you put two or more ants with different algorithms sharing the same space? do they cancel eachother, or something else emerges?

how about a mandelbrot algorithm but in 3d?

4:00 looks a bit like brownian motion

it 3d wow amazement

Any chance you can make the source code available?

What about the Konami code (up, up, down, down, left, right, left, right)?

You could probably generalize this to even higher dimensions, imagine a 4d Langton's ant!

DRLU ruleset hasn't highway'd for 1500000 steps

It's a bit like randomly putting DNA building blocks together to "see what happens", (we call this "science") then occasionally modify them at random. Eventually, with luck the pattern becomes self-sustaining and we get something which will grow in a Petri dish, which we might call a bacterium.

imagine switching the color blocks with environment blocks, assigning the rarer colors as more valuable blocks, like diamonds, bonus chests/monster spawners and water blocks. Then playing A survival game on the ant island as it grows. the ant may bury you alive by passing through you, and it'd cut through your house, which would also alter it's course.

i dont like things like langton's ant and conway's game of life cuz i dont like things that just expand with no end

Differential opacity with light-emitting cells?!

Just asking, can you tell me the link to the Langton’s Ant thing?

6:00 DOWNWARD SPIRAL DOWNWARD SPIRAL also how did you get to those combos

By the power computer science, I shall bring life to art... LITERARY!!!!

Can we expect something like this from nanobots?

you can see patern that same as dna

The next time i make a bedwars server in minecraft ill use this ant to generste

Wow

Minecraft self building sculpture

Are those last few really chaotic, or will they also eventually make highways? I know that the highway in the original ant algorithm is a stable attractor and will happen no matter the initial conditions, but is that true for all alt algorithms?

This i believe to be what was known as jacobs ladder and i know this will be the most used tool soon i broke it

Now make it in 4 dimensions

oh thats what it is

haha highway go BRRRRRRRRRRRRRR

Me trying to make a house in minecraft

Too slow. You should have sped it up.

minecraft le gusta esto

4:11 Dream or TapL bridging in Minecraft...