I have such an interesting observation: if I take a square grid and rotate it over itself by atan(3/4) , it forms a structure which has four axes of reflection symmetry:
The resulting structure is really mesmerizing, I see a lot of symmetric shapes in it: octagons, stars, rhombuses. And all of them appear inside this structure in different sizes, namely scaled by an integer factor:
Also looking at minimal periods, I notice that exactly the same structure I can create from rhombus grids, put over itself at 90 degrees. Namely rhombuses which have height of double of its width.
And the same structure, only with one additional square grid over it, I can create from a parallelogramm. Once I have made a question about this parallelogram (Very special geometric shape - parallelogram (No name yet?))
To spawn it from parallelogram I copy-reflect the parallelogram grid and then copy-rotate the whole by 90 degrees:
- How this particular structure is classified, or named?
- Do you know of any articles about it or any applications?
To be exact, I made up two structures, but since they are almost the same, I hope this does not add much confusion.