I mentioned earlier about the odd-odd grids not being new, but there’s more for the math nerd (this may scare others, sorry!) You can “multiply” an (a, b) grid and a (c, d) grid together to get a larger (ac - bd, ad + bc) grid. The studs in this grid are actually subsets of the studs of either original grid. So some grids are “prime”, while some can be “factored”, i.e. they are subsets of denser grids. The odd-odd examples are all not prime, they are the “product” of something with a (1,1) grid. And the reason the “super sugar grid” is super is because it’s the product of the (1,2) grid with itself. This is actually the study of prime numbers in the Gaussian integers (complex numbers where both components are whole numbers) which is a freakin awesome thing to naturally come up from Lego!!!
Seeing this used with SNOT is actually very interesting. I'd love to see how the 45 technique works with SNOT too, and maybe even how all three techniques can work together, 45, Sugar, AND SNOT.
Bringing this back to your city building, the sugar grid on the wall could be useful for something like those angled wall panels along subway escalators.
A question: Having established sugar grids & sugar shifts... can you apply LDU to your grids in order to achieve more degrees of rotation? With that in mind, is there a mathematical formula that can be applied to these creations?
I think the LDU’s would merely have the potential to shift the sugar grid around the space (translate not rotate). And so I think the angle would not change. But I may be wrong. However, if you keep expanding the sugar past the 10x10 limit set in his videos you could achieve more angles. I hesitate to say that ANY angle is possible though.
The issue is with going down to the LDU level for the studs is that the plates still only have the same attachment positions. So unless you modify the underside of the plate, you won't get any more angles. What it might allow you to do though is to get a few of those that are only possible in 40 by 40 or whatever into the 10 by 10 size - potentially.
@ totally!! I didn’t think of that!! That should work because all you are after is the ratio (in the video you can see at 3:55 that 3:6 is the same as 1:2, as he mentions, but also the same as 2:4), so there may be some weird “reduced ratios” you could create to replicate larger sugar grids using LDU techniques to offset the studs. Neat!
I feel like I’m missing some crucial information in order to actually understand those grid ratios sizes. Are we talking about plates with those length and width sizes that fit on to those ratios? Or are we still talking about a plate that is 2 studs wide, and then the corresponding length that matches to that two studs wide plate/brick.
The odd sugar grids actually aren’t new! The (1,3) grid is just the (1,2) grid with half the studs missing (the extra stud is in the center of the square in your mock up). In general a (m, n) grid with both odd numbers is just a ((n - m) / 2, (n + m)/2) grid.
You are making the same mistake as I did on Discord. 3/1 is actually standard sugar grid(1/2) without central stud. If (a/b) is sugar grid, then (c/d) will be the same grid without stud if a
It's funny because other person with triangle avatar was first or very close. It's weird it happened twice! ua-cam.com/video/TIWZd2xrDoY/v-deo.html&lc=UgwpupMZhoae_65iYKh4AaABAg
ive got a bunch of SNOT techniques working in my nose rn
Lol
winter…🙄
The sugar grid lore gets deeper every day
Never ends lol
I mentioned earlier about the odd-odd grids not being new, but there’s more for the math nerd (this may scare others, sorry!) You can “multiply” an (a, b) grid and a (c, d) grid together to get a larger (ac - bd, ad + bc) grid. The studs in this grid are actually subsets of the studs of either original grid. So some grids are “prime”, while some can be “factored”, i.e. they are subsets of denser grids. The odd-odd examples are all not prime, they are the “product” of something with a (1,1) grid. And the reason the “super sugar grid” is super is because it’s the product of the (1,2) grid with itself.
This is actually the study of prime numbers in the Gaussian integers (complex numbers where both components are whole numbers) which is a freakin awesome thing to naturally come up from Lego!!!
Very interesting!
The shifted sugar grid and snot sugar grid strikes me as a novel way to make big paving tiles with narrow gaps between them while remaining fixed
The sugar grid: the gift that just keeps giving XD
No that's the Jelly of the month club :)
Seeing this used with SNOT is actually very interesting. I'd love to see how the 45 technique works with SNOT too, and maybe even how all three techniques can work together, 45, Sugar, AND SNOT.
Bringing this back to your city building, the sugar grid on the wall could be useful for something like those angled wall panels along subway escalators.
One Lego video a day on Christmas is a treat neither my parents when I was 8 gave me :) Wish you the best holidays!
I will be taking a short vacation after Christmas but have a few pre scheduled videos in there to hold you over.
I see that 1x1 tile on the thumbnail XD
2:30 Simplify things by eliminating the mirror images. Only keep the versions with a stud towards the [left or right] of the top side.
A question:
Having established sugar grids & sugar shifts... can you apply LDU to your grids in order to achieve more degrees of rotation?
With that in mind, is there a mathematical formula that can be applied to these creations?
I think the LDU’s would merely have the potential to shift the sugar grid around the space (translate not rotate). And so I think the angle would not change.
But I may be wrong.
However, if you keep expanding the sugar past the 10x10 limit set in his videos you could achieve more angles. I hesitate to say that ANY angle is possible though.
I don't think LDU will help with the rotation. But maybe placement on the grid. As for formulas I let's others work tgat out it's beyond my brain lol.
I don't think LDU will help with the rotation. But maybe placement on the grid. As for formulas I let's others work tgat out it's beyond my brain lol.
The issue is with going down to the LDU level for the studs is that the plates still only have the same attachment positions. So unless you modify the underside of the plate, you won't get any more angles. What it might allow you to do though is to get a few of those that are only possible in 40 by 40 or whatever into the 10 by 10 size - potentially.
@ totally!! I didn’t think of that!!
That should work because all you are after is the ratio (in the video you can see at 3:55 that 3:6 is the same as 1:2, as he mentions, but also the same as 2:4), so there may be some weird “reduced ratios” you could create to replicate larger sugar grids using LDU techniques to offset the studs. Neat!
I feel like I’m missing some crucial information in order to actually understand those grid ratios sizes.
Are we talking about plates with those length and width sizes that fit on to those ratios? Or are we still talking about a plate that is 2 studs wide, and then the corresponding length that matches to that two studs wide plate/brick.
9:51 HA! Gotem!
28 seconds, "watch this video here", but no card appeared, somebody forgot it ! maybe build some reminder from lego bricks ?
The card is there it's just not been working at times. Might be a UA-cam or a browser issue.
The odd sugar grids actually aren’t new! The (1,3) grid is just the (1,2) grid with half the studs missing (the extra stud is in the center of the square in your mock up). In general a (m, n) grid with both odd numbers is just a ((n - m) / 2, (n + m)/2) grid.
You might be correct lol I have to look into that one.
Just a hunch but I bet the duplicates make the pattern into 4 Sierpinski Triangles
Not sure what that is lol
@@bricksculpt Like a self similar triforce and thinking about it it would probably be 8
I think the shape described is an "Euler's orchard"
You didn't put up any link for the earlier sugar video when you said "Please go here"
I don't see videos or pop up videos in stuff because I'm using Firefox not even during an exit parts of videos
It must not have saved. Thanks ill get that fixed.
You are real LEGO Sugar Daddy!
Basically
MORE SUGARRR
Def Leppard - Pour Some Sugar On Me :D
THATS the one. The 2x2 jumpers inward. I need to experiment with that with rock outcroppings builds... 🪨
Oh that would work well!
You are making the same mistake as I did on Discord. 3/1 is actually standard sugar grid(1/2) without central stud. If (a/b) is sugar grid, then (c/d) will be the same grid without stud if a
"but wait, there is more"
I remember that line from one of the “scary movie” movies.
I don't know how I didn't connect the dots from watching previous video!
Probably because we’re working with studs. Forgive me, but I just had to make that bad joke. 😅
I figured out a while ago you can stack 4x4 macaroni bricks offset like a staircase, which makes a sugar grid
Poursome sugar on me
Fresh video
6:26 Censorship in action.
You know that it’s all in your head.
First, finally
Did anyone ask? Does anyone care?
It's funny because other person with triangle avatar was first or very close. It's weird it happened twice!
ua-cam.com/video/TIWZd2xrDoY/v-deo.html&lc=UgwpupMZhoae_65iYKh4AaABAg