This is pretty simple. Notice that the chessboard is divided by lines parallel the X and Y axes, just as an ordinary chess board is. The only difference is that on an ordinary board the line spacing is uniform - all spacings equal.

In this case the distance between the parallel lines varies according to some formula - such as a sine wave.

To reproduce this you only need to create 1/4 of the board and then replicate that three more times.

1. To do this produce a line and replicate it a number of times - looks like 10. Then arrange these lines parallel but with increasing spacing according to whatever formula you want to use).

I used sine(10), sine(20), sine(30), ... sine(80) and sine(90).

2. Select 9 of the lines on the left and mirror them around the 10th line. This produces an odd number of lines (19) and an even number of spaces (18).

3. Select all lines, duplicate them and rotate 90 degrees.

4. Overlay the two sets of lines.

5. Now change to a new layer, lock the original layer, and use Hatch Fill to fill in the spaces.

6. Select all of the hatch fills and duplicate them four times, aligning the corners.

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To get exactly the same pattern as the original example you need to figure out the way he created the spacing. I suspect it wasn't mathematical, but was done geometrically, but I could be wrong.

You can use any spacing formula and get different results with each.

Phil