For more examples please see my related question on MSE: Interesting tiling with a lot of symmetrical shapes
This is achieved by rotation of square grid over itself by atan(3/4).
Resulting grid is a base for a whole class of beautiful tilings, see examples in the linked question.
Playing with this grid I can make up many tilesets and most interesting is, that they can act in 8 directions (4 axes).
Namely I can represent contiguous equal-width lines in all 8 directions and respectively all shapes formed by these lines.
Resulting shapes have smooth transitions, no gaps and are 'scalable'.
On the other hand such tilesets are very simple and with low amount of unique tiles. So in other words, it is a whole nugget of interesting applications, e.g. in vision and typography.
Still I was not able to find any concrete source related to this tiling class.
So can you recommend any good sources dedicated to this phenomenon?
It has some connection to Pythagorean tiling, namely a Pythagorean tiling with 1:2 square ratio can be used to construct this tiling.
After drawing lines all over the plane it results in the above described tiling. Here it is painted in two colors: