[kevinwang]

Squares, but each row of squares has a random offset

[irishsultan]

That is a periodic tiling (just think about what happens if you follow the tiling along the rows instead of along the columns, you'll periodically see the same pattern).

[kevinwang]

No, you wouldn't necessarily

[irishsultan]

https://en.wikipedia.org/wiki/Euclidean_tilings_by_convex_re...

It's listed as a periodic tiling. If you move the whole plane one square to the left or right you'll find that everything fits into place nicely, making this a periodic tiling.

[kevinwang]

Hm, I'm not knowledgeable about this subject but this seems like the offset on each row is NOT random, but it's instead repeating. Imagine instead that each time I added a new row, I chose the offset to be, say, a completely new value.

[irishsultan]

Doesn't matter, because your new row will still be offset with the same random value to existing rows after moving one square to the left or right.

[Terr_]

Or triangles, with similar "slide along the seam" changes.