Will the center octogon ever repeat if the pattern continues?

[glad bay]

I don't think it will ever repeat because the diagonal is sqrt(2) as large as the side length of the square, and sqrt(2) is irrational

so that exact center pattern will never repeat again

[green garden]

no giving away the answer @glad bay

[glad bay]

whoops lol

I don't think there's a specific word

Do you know how to code at all? I think this type of pattern would be relatively easy to generate if you do

[green garden]

I would consider this problem “analytic” geometry, which you may or may not have learned in geometry class yet

well it’s not repeating

[glad bay]

yeah I wouldn't consider this a "fractal"

this is more like a "tiling"

which is when you cover the plane with similar looking objects

in your case you have two different tilings, one on top of the other

haha it's not very unsolvable considering we just solved it

when they connect, the lines wouldn't line up

I'm pretty sure I understand your problem perfectly? The answer is just no, it will never repeat

45° from each other

It doesn't either, yeah

It will never repeat no matter how you move the two grids across each other

[glad bay]

^

The two squares at the origin share a center

And are at an angle of 45° to each other

[green garden]

to code this up, you would need to ascribe coordinates for everything

so for example, the central octagon is at the origin (0,0)

then you have a square at every point (m,n) for integers m,n

can you guess where the diagonal squares will be located?

[dawn basin]

Yes this describes the problem correctly and the answer is a fairly straightforward no

[cunning canopy]

Won't u have to deal with floating point imprecision? Using code to calculate this seems difficult bc it involves an irrational

[glad bay]

I assume they just want to draw it, in which case some imprecision is probably acceptable

[ripe quail]

probably won't, otherwise √2 times some integer would have an integer result, which is possibly impossible due to some math theorem other than the case shown in the picture where that integer is 0

√2 is the length of the diagonal of that square if assuming the sides are 1

but it doesn't matter if you assume it different, it would still boil down to this problem

[dawn basin]

The most straightforward way to represent this mathematically is by simply giving the center points of the horizontal squares integer coordinates

You can then find the center points of the diagonal squares from this

I also don't see anything of cryptographic interest here

The general basis of cryptography is using functions that are easy to calculate in one direction but are phenomenally difficult to invert

For example, it is easy to multiply numbers but extremely difficult to find prime factorisation

In this case the coordinates of each of the two grids are simply linear subspaces of the plane

Linear problems are just about the easiest imaginable problems