8:33 these diagonal squares made visually are my absolute favorite! I can't decide if I like them or the more complex lime shown later better. it's so refreshing to see some new patterns.
This video inspired me to see if there was a way to create a hexagonal or triangular pattern on the typical flat square grid, and I stumbled upon a proof of why it's completely impossible. It all has to do with the fact that the "period" of repetition along any given line in the hexagonal grid (so how long you have to travel before getting back to a "congruent" point) will always be an *irrational* multiple of the "period" along a line 90 degrees away from the original. I had a sort of guess at the idea that if it was a rational, fractional relationship, it would be possible to express it on a square grid using a texture pack or something like that, but in the case of the hexagon it always seems to involve the square root of 3 somehow.
Nice video ! To really see clearly the "hexagonal" pattern, and/or if you want to see Minecraft with an isometric projection (where every edge of every block has the same length), there is a mod (well a few in fact) called Mineshot Revived (by Pascal Roeleven) you can use to change the camera perspective ! There is also top/bottom/side view, and you can use that mod to take huge screenshots of your world ;)
with the discovery of the 13 sided shape that tiles forever without repeating, im now wondering if something like that is possible in minecrafts grid system, or at least how to make shapes that eliminate lines of symmetry and rotation
A mathematician named Glenn C. Rhoads has actually put out multiple papers over the last 20 years about planar tilings when the tiles are built up from squares (or from triangles or hexagons). In fact, Dr. Rhoads did their PhD thesis specifically about whether a tile made of squares could solve the problem that this recent discovery solved! Here's a link: www.proquest.com/openview/9b391d50891e8b93ee99a03d2cc0f46a/1?pq-origsite=gscholar&cbl=18750&diss=y
There's a lot of ways to do aperiodic patterns with shapes that can otherwise tile periodically, but if you want to do shapes that can only tile aperiodically, you'd probably be limited to some sort of set of Wang tiles built out of sets of blocks.
there are a lot of possibilities using the map system. I'd love to see what you could make with a custom 128x128px map You could probably faithfully recreate some of escher's tiling designs
You should put these videos in a playlist! i had to search through your entire channel to find a way to watch them in order :P PS: why does the x in episode y of x keep changing XD
@@whitestonejazz oh thank you guess I’m blind- very cool! if you want you could make one of the showcases on your home page into the «playlist showcase» thing so blind people like me find the different serieses easier ( it’s in the customization tab in acc )
Is there a reason they’re called reds and blues? I know the reds reflect (ha) the reflections, and the blues reflect the rotations is there reason for them being named reds and blues?
It's just a memory trick suggested in the textbook I'm reading. The full nicknames are "REflecting REd" and "trUE blUE" so that each nickname has two matching letters, in the front of the words or on the backs of the words. I colored the hybrids green just so that the 3 families of patterns would be colored red-blue-green like a pixel
Игры
Thanks for mentioning my cube corner idea!
8:33 these diagonal squares made visually are my absolute favorite!
I can't decide if I like them or the more complex lime shown later better.
it's so refreshing to see some new patterns.
This video inspired me to see if there was a way to create a hexagonal or triangular pattern on the typical flat square grid, and I stumbled upon a proof of why it's completely impossible.
It all has to do with the fact that the "period" of repetition along any given line in the hexagonal grid (so how long you have to travel before getting back to a "congruent" point) will always be an *irrational* multiple of the "period" along a line 90 degrees away from the original. I had a sort of guess at the idea that if it was a rational, fractional relationship, it would be possible to express it on a square grid using a texture pack or something like that, but in the case of the hexagon it always seems to involve the square root of 3 somehow.
as a person who can't look at graphs without getting a headache, watching this series is a challenge
6:52 🎵 I'm my own grandpa~🎵
This series is great, and would love to see ep 6, 7, and 8 one day 😀
Since you've started this series the floors for all my bases look so much better!
Nice video !
To really see clearly the "hexagonal" pattern, and/or if you want to see Minecraft with an isometric projection (where every edge of every block has the same length), there is a mod (well a few in fact) called Mineshot Revived (by Pascal Roeleven) you can use to change the camera perspective ! There is also top/bottom/side view, and you can use that mod to take huge screenshots of your world ;)
So you're telling me I can use Minecraft to make my engineering sketches?
with the discovery of the 13 sided shape that tiles forever without repeating, im now wondering if something like that is possible in minecrafts grid system, or at least how to make shapes that eliminate lines of symmetry and rotation
That tile is based on a hexegon, so it would be difficult
A mathematician named Glenn C. Rhoads has actually put out multiple papers over the last 20 years about planar tilings when the tiles are built up from squares (or from triangles or hexagons). In fact, Dr. Rhoads did their PhD thesis specifically about whether a tile made of squares could solve the problem that this recent discovery solved! Here's a link: www.proquest.com/openview/9b391d50891e8b93ee99a03d2cc0f46a/1?pq-origsite=gscholar&cbl=18750&diss=y
There's a lot of ways to do aperiodic patterns with shapes that can otherwise tile periodically, but if you want to do shapes that can only tile aperiodically, you'd probably be limited to some sort of set of Wang tiles built out of sets of blocks.
your videos are so unique i love it. minecraft never gets old :)
8:42 awww it looks like a heart! I'm sending my crush this hehe
there are a lot of possibilities using the map system. I'd love to see what you could make with a custom 128x128px map You could probably faithfully recreate some of escher's tiling designs
Caught it! V excited :)
Excellent video
Analogously the family tree seems more like a family carbon nanotube
You should put these videos in a playlist! i had to search through your entire channel to find a way to watch them in order :P
PS: why does the x in episode y of x keep changing XD
There should already be a playlist: ruclips.net/p/PLH9ALTdVQllFUsHYTyIETYCoOYU4roVPw
also each episode I guess at how many more there will be haha. That's why it changes
@@whitestonejazz oh thank you guess I’m blind- very cool!
if you want you could make one of the showcases on your home page into the «playlist showcase» thing so blind people like me find the different serieses easier ( it’s in the customization tab in acc )
PS looking forward to next video, no matter how many «out of x» parts it has :P
You should try this but for ways that sothing can tile.
09:06 not steering whiles, but cog whiles!
the cubes would look less cubey in orthographic mode
you'd need to make it big though
Is there a reason they’re called reds and blues?
I know the reds reflect (ha) the reflections,
and the blues reflect the rotations
is there reason for them being named reds and blues?
It's just a memory trick suggested in the textbook I'm reading. The full nicknames are "REflecting REd" and "trUE blUE" so that each nickname has two matching letters, in the front of the words or on the backs of the words. I colored the hybrids green just so that the 3 families of patterns would be colored red-blue-green like a pixel
@@whitestonejazz ahh!! I see! Thank you so much!!
:D eeee
I don't think you need to use cubes to make hexagons. You can just stagger the blocks. Don't think so literally.
Nice I personaly liked the redstone video more where u made the most directional redstone machine lol
found the floor tile hater
@@user-dx4rx3bt2l hahahaha
bro how many of these will there be the count keeps changing lmao
it's partly cause I'm debating whether to do 3D patterns or not
@@whitestonejazz that would be very interesting
🤓
…did someone just say *_origami_*