Creating a specific tileable pattern mask

Question

I am trying to create a tileable mask for the pattern above. I tried to arrange the lines with an Voronoi Texture, with 0.0 randomness and Chebychev Distance Matrix as well as an Color Ramp to get hard lines:

Like this and with Vector Math Nodes like Add and Multiply and finally Mix Color Nodes I tried to arrange the lines, but even after many attempts, I just did not get it tileable, like in the first picture above.

Now I'm out of ideas, how to achieve that. Does somebody has an idea?

Here is what I got so far:

Answer 1

I would use generate texture coordinates instead of object.

From that, use some value to determinate the subdivision scale, modulo and scale the coordinates from it.

Then use 'vector absolute' node as the figure is symmetrical in both X and Y.

Next:

From top to bottom:

Big diagonals are where X equal Y.

Inclined smaller diagonals are where 2 X equal Y.

Shifted lines parallel to the previous where 2 (X - 0.25) equal Y.

Centered horizontal lines are where Y equal 0 but for X less than 0.25.

Bottom/top horizontal lines are where Y equal 0.5 for X greater than 0.25.

Vertical lines are for X equal 0 or 0.5.

(Blender 4.0)

I realized you may effectively want to use object coordinates in order to have a regular wallpaper whatever the object is.

To do that with the previous settings, modify the begining like so:

Scale down the coordinates with some factor (e.g. 1/64) and get absolute value. The next steps are the same as before.