Quick look, don't sue me if I'm wrong! :D

Appears to be a diagonal tiling of square sub-tiles with overlap. So THIS specific pattern must meet the condition t*(p-o) = s
Where t = subtiles, p = subtile size, o = overlap & s = tile size.

So in your case 4*(5-1) = 16 works (as does 8*(5-1) = 32)

16 and 32 only has 2 as primefactors and can only be divided by 2 or n^2. Which means both subtiles and (subtile size - overlap) must be divisible by n^2.

Which means the only 1 pixel overlap possibilities are
2 * (17-1) = 32
4 * (9-1) = 32
8 * (5-1) = 32

I thought this was going to be simple, but I guess not :/

DB, I followed your rule here, right? The tile in my example has a width of (9-1) and a height of (8), so it's square and should fit in a 16x16 tile...
Yet I found this shape by randomly playing around, which only fits in a 33x66 tile... :o



(edit: posted before seeing reply above)

I suspect we've all misunderstood what DB meant by "overlap". I'm not going to guess.


All this is is a brick pattern turned 45 degrees. So, if one diagonal is split into an even number of rows (just as you'd divide a regular brick pattern into an even number of rows along the vertical), and the other diagonal is split into some number of brick "widths" (just as you'd have an integer number of bricks along the horizontal in a regular brick pattern), you'll have a working pattern. That the bricks intersect with a sawtooth pattern is merely cosmetic and doesn't impact the math at all.
In other words, I recommend approaching this from the tile down to the cell, rather than from the cell up to the tile.

For example:

On the left, I made four rows and plopped a "vertical" cell boundary every 4 pixels along the other diagonal (4 divides nicely into 32). Since everything divides nicely, it tiles seamlessly. On the right, I just added the sawtooth pattern.

@DawnBringer Oh yeah ! It makes sense now ! Thanks a lot !