It might be interesting to see the "pegs" transformed into "threads" that go over/under in parallel lines. Then the cloth would be flexible and not nailed down.
My immediate thought seeing this is that you should make a knot that starts on the lower layer, and then through a few twists on posts, moves up to the top layer. So multi-players can move between layers
It's crazy how at the end of the day i understand what you are explaining but you are clearly thinking it in a completely different way than how i would understand it. It could be because you understand a lot of math behind it that i don't have, but this is really interesting !
So, is the next video in this series gonna be on the diagonal options for knots? (By making the pegs along a diagonal, we can translate this to triangles/hexagons in the exact same way we could with the floor patterns. You might think this doesn’t really do anything, as we already had the hex/regular triangle patterns with floor problem, and those would be preserved in the knot problem, but when we abstract the mentioned “rotational symmetries” of the knot problem, we see that they are actually now *lines* around which rotation occurs, rather than points. This is important, because it allows for intersecting lines of rotation, where in the floor problem, the points of rotation projected into a 3D space would be parallel. One last note; I don’t think the knot problem interacts with this much, but the lines of reflection generalize to planes of reflection in 3D space, allowing for more complicated systems of intersection… Or does it? Not many regular polyhedron tile a 3D space, but they need not be regular.
@@whitestonejazz Ooh, cool, Archimedean polyhedra are cool. In the floor problem we saw that 90/45/45 triangles were able to tile, and they were non-regular polygons, so regularity doesn't appear to be a limitation. I wonder how this will extend to 3D. I honestly have no idea.
Reminds me of lace or weaving more than cloth, but very neat! Have you heard of aperiodic tilings? The "hat" was just discovered, but might be awkward in minecraft. Maybe a set of wang tiles would be easier.
Oh I love this! Weaving is where coding began (hyperbolic but true)! Looms were one of the first machines to ever become automated, using punch cards, so you can imagine a hole or no hole (up or down for the weave) is the equivalent of 1s and 0s, a connection or no connection! The first binary code :D You've made it go full circle! 👏 :D Btw, you should 💯% look up How people make Lace by Hand, it's kind of exactly what you're doing!
Mogswamp suggested your channel, and he was so right to do so. This is awesome. I love math, Minecraft, and learning! This is awesome! Keep it up brother!
I'd like to see a version of this with some connections between the top and bottom layers. Especially if there's at least one twisty connection that forms a staircase!
here in croatia and generally in the balkans there is a traditional thing made out of white strings usually a circle pattern and its put on things (old tvs) best example
Looking at the thumbnail, I thought it was either a mod or a mc clone that implements a new type of logic that is more akin to irl electronics than redstone
After seeing you extend symmetries into the third dimension, I wonder how many symmetries would exist in a 4 dimensional cube world (like the game 4d miner)
@@whitestonejazz Oh thanks! I saw it at the end, but I thought this still could be helpful to someone else, and I thought the wool texture was different, you were actually using concrete blocks then. I didn't expected you to respond. Thx 😃
A lot of these patterns remind me of the metal organic frameworks and coordination polymers I would see in grad school. Have you looked into Crystalographic symmetry at all?
@@whitestonejazz I'd love to recommend you a textbook, but all of mine are crystallography focused so gloss over the math behind the symmetry in favor of illustrations and instructive examples for chemists
I read "The Symmetry of Things" recently by Conway, Burgiel, and Goodman-Strauss and had a great time. There was also a braid groups textbook that stuck with me from a few years back but I can't remember the name. Pretty sure it was a classic yellow Springer book tho
@@1T1T1 kind of. You have to build the pattern at a weird angle to get triangular symmetry. There's a clever way to get 3-fold spin symmetry by spinning the XYZ coordinates one after each other. So X becomes Y and Y becomes Z and Z becomes X
There's another video series on floor patterns on this channel where the math is explained better.. But in more technical terms, my textbook is about the planar symmetry groups (called "wallpaper groups") and the color-symmetries they can have.
Игры
It might be interesting to see the "pegs" transformed into "threads" that go over/under in parallel lines. Then the cloth would be flexible and not nailed down.
Intel wiring transistors in CPUs:
Or: copper quilt programming in old nasa tech
a lot like wire wrap
@@nerdiconium1365 Programming used to be thought of as a "woman's job".
My immediate thought seeing this is that you should make a knot that starts on the lower layer, and then through a few twists on posts, moves up to the top layer.
So multi-players can move between layers
It's crazy how at the end of the day i understand what you are explaining but you are clearly thinking it in a completely different way than how i would understand it.
It could be because you understand a lot of math behind it that i don't have, but this is really interesting !
Your idea of this "cloth" stuff was so popular, they made it in real life. Where would society be without you?
For more patterns ask your grandma
How are you so charismatic
So, is the next video in this series gonna be on the diagonal options for knots?
(By making the pegs along a diagonal, we can translate this to triangles/hexagons in the exact same way we could with the floor patterns.
You might think this doesn’t really do anything, as we already had the hex/regular triangle patterns with floor problem, and those would be preserved in the knot problem, but when we abstract the mentioned “rotational symmetries” of the knot problem, we see that they are actually now *lines* around which rotation occurs, rather than points. This is important, because it allows for intersecting lines of rotation, where in the floor problem, the points of rotation projected into a 3D space would be parallel.
One last note; I don’t think the knot problem interacts with this much, but the lines of reflection generalize to planes of reflection in 3D space, allowing for more complicated systems of intersection… Or does it? Not many regular polyhedron tile a 3D space, but they need not be regular.
The book I have actually lists off all the space-filling "Archimedean polyhedra" (= 3d polyhedra that have only regular polygons as sides)
@@whitestonejazz Ooh, cool, Archimedean polyhedra are cool. In the floor problem we saw that 90/45/45 triangles were able to tile, and they were non-regular polygons, so regularity doesn't appear to be a limitation. I wonder how this will extend to 3D. I honestly have no idea.
what the hell a minecraft video im watching mentioned group theory
amazig
The nature of human humanity is that, given time math and resources, someone will reinvent textiles in every way that it can be reinvented
Reminds me of lace or weaving more than cloth, but very neat!
Have you heard of aperiodic tilings? The "hat" was just discovered, but might be awkward in minecraft. Maybe a set of wang tiles would be easier.
Your videos are so interesting bro. So cool to see recreational math applied in my favorite game.
Oh I love this! Weaving is where coding began (hyperbolic but true)! Looms were one of the first machines to ever become automated, using punch cards, so you can imagine a hole or no hole (up or down for the weave) is the equivalent of 1s and 0s, a connection or no connection! The first binary code :D
You've made it go full circle! 👏 :D
Btw, you should 💯% look up How people make Lace by Hand, it's kind of exactly what you're doing!
2:23 Ah yes, my favorite superpower.
*Axel Vision!*
It's like telekinesis, but you can only twist things in place.
I love patterns and stuff like this, I can already see some kinda bow and arrow sumo situation for a multiplayer game
I swear, this is the place I swing around like a monkey in my dreams.
Definitely going to take inspiration from this to make some fancy game platforms lol, amazing find lovely stuff as always!
i love the meers
like little meercats
a mere mirror
You are the most unique minecraft youtuber
babe wake up WhiteStoneJazz uploaded
i like the chill music underscoring the audio
Mogswamp suggested your channel, and he was so right to do so. This is awesome. I love math, Minecraft, and learning! This is awesome! Keep it up brother!
nice
art
Might be cool to see this combined with insulated skulk-sensor wiring to form a (likely impractical) wire network.
Love it
I'd like to see a version of this with some connections between the top and bottom layers. Especially if there's at least one twisty connection that forms a staircase!
Good vid !
The music was a bit too loud compared to the voice I think, but that may be just because of my earpods
audio quality is my nemesis. thanks for the feedback
Cool vid!
I love Minecraft, this is awesome
Can you show what it looks like on a map. I think it could look really cool
awesome
Automated textile manufacturing machines (jaquard loom) are considered the grand grand grand parents of modern computers. How beautiful is that
here in croatia and generally in the balkans there is a traditional thing made out of white strings usually a circle pattern and its put on things (old tvs) best example
With the nails, it reminds me of Bobbin Lace making. Especially with the twists explanation around 5:30.
Watching this video made me feel as if I'm high af. Very interesting stuff!
Looking at the thumbnail, I thought it was either a mod or a mc clone that implements a new type of logic that is more akin to irl electronics than redstone
Chris has taken up knitting
After seeing you extend symmetries into the third dimension, I wonder how many symmetries would exist in a 4 dimensional cube world (like the game 4d miner)
You would have 4
Very geud
omg, imagine this but with immersive portals mod so you can easily add to it without having to copy and paste it everywhere else
for the cloth without the pegs, wouldnt that basically be deciding the grain of the cloth?
1:05 lol i didnt realize they were nails and it would spin around at all
I don't know if I wouldn't consider it cloth, since cloth normally you can't see the gaps between the threads. I'd call it a web.
I'm sure you already know this, but the knot tiles you made here are called "tangles" (in knot theory).
Me just curious to what it would look like on a Minecraft map 👀
the nails look like leg hairs to me and I can't unsee it
"Morris Escher", I have never heard him referenced by first name.
Time to world download and turn on the acid shader
I wander if you could make Borromean rings or links into a pattern like this.
What are your shaders and texture pack? It seems to help understanding it and it looks like the Minecraft promotional texture.
Complementary Shaders using the Iris mod
@@whitestonejazz Oh thanks! I saw it at the end, but I thought this still could be helpful to someone else, and I thought the wool texture was different, you were actually using concrete blocks then. I didn't expected you to respond. Thx 😃
Reminds me of pipes in Mario almost
A lot of these patterns remind me of the metal organic frameworks and coordination polymers I would see in grad school. Have you looked into Crystalographic symmetry at all?
I've learned about them a little bit. My next goal is to just learn more about 3D symmetries in general
@@whitestonejazz I'd love to recommend you a textbook, but all of mine are crystallography focused so gloss over the math behind the symmetry in favor of illustrations and instructive examples for chemists
Do you suggest any reading material about knots and patters?
I read "The Symmetry of Things" recently by Conway, Burgiel, and Goodman-Strauss and had a great time. There was also a braid groups textbook that stuck with me from a few years back but I can't remember the name. Pretty sure it was a classic yellow Springer book tho
Ah yeah, another perfectly okay and normal video
Actual CPU architecture
Chris did you try to make flower of life pattern?
nah but I looked it up now. will try it when doing more 3d patterns
@@whitestonejazz always had in mind to try to make it but never gut to it
perfect circular geometry in at 3d game
is it even possible ??
@@1T1T1 kind of. You have to build the pattern at a weird angle to get triangular symmetry. There's a clever way to get 3-fold spin symmetry by spinning the XYZ coordinates one after each other. So X becomes Y and Y becomes Z and Z becomes X
neat channel!! i would love to see more like these in my feed :))) sub
Macrame!
Reminds me more of a net than a cloth lol, looks cool asl👍
I think one of the greatest intelectual crimes has been the neglect of the math of textiles (maybe) due to the gendering of the discipline
how to install fabric mc
Crochet weaves
Wait was that : under over, or over under... 🤦🏾♂️
Fabric
You keep talking about that this is related to math. could you clarify and explain what you mean?
There's another video series on floor patterns on this channel where the math is explained better.. But in more technical terms, my textbook is about the planar symmetry groups (called "wallpaper groups") and the color-symmetries they can have.
The fabric pattern
wouldn't the word you're looking for be called a textile?
short side note: your mic is too sharp at high frequenzies
thank you so much. I spend like 30 minutes on every video just listening to the audio saying "I know this doesn't sound good but I don't know why"
@@whitestonejazz hope it helps
I understand nothing from it.
Hey man, do you have a Discord server for your followers? It would be fun to interact with others that are interested in this stuff and yourself.