Unicode codepoints 0x2596–0x259f can help you draw primitive graphics by offering all the combinations of on or off for the four quadrants of a glyph. They're available in this order:
▖ ▗ ▘ ▙ ▚ ▛ ▜ ▝ ▞ ▟ 00 00 10 10 10 11 11 01 01 01 10 01 00 11 01 10 01 00 10 11
Actually, that's only ten of the sixteen you need for the full set. The remainder are scattered a bit:
0020 2580 2584 2588 258C 2590 ▀ ▄ █ ▌ ▐ 00 11 00 11 10 01 00 00 11 11 10 01
...but I think I more or less understand why they're scattered. Space is a leftover from ASCII, and the others sit in very pretty patterns in codepoint-space. The lower half block sits in a sequence of seven increasingly-tall blocks (terminating with the full block), and the left half block sits in a sequence of seven decreasingly-wide blocks (beginning with the full block), while the upper half and right half hang out at the respective ends of those sequences.
But how was the order of the first ten mentioned in this question chosen? Some hypotheses I pondered but rejected:
The first three all have just one of the four quadrants "on"... but the fourth one does not follow this pattern, with the final single-quadrant codepoint lying near the end of the sequence. So we don't group them together by quadrant count.
If you think of the bottom left quadrant as the least significant bit, followed by the bottom right, top left, and top right, then the first three could be understood as simply "counting up" (skipping over the blocks that are scattered around the rest of codepoint space), but then the fourth one in that pattern actually appears in position five instead.
If you look at just the top left and top right quadrants, it looks like a nice clean gray code. But the bottom two bits don't appear (to me) to be continuing that pattern. For example, I would expect 00/01 to transition through 10/01 to 10/00, but 10/01 appears later in the sequence.
There are ten of them, which factors to 2×5; perhaps laying them out that way reveals something?
▖ ▗ ▘ ▙ ▚ ▛ ▜ ▝ ▞ ▟ ▖ ▗ ▘ ▙ ▚ ▛ ▜ ▝ ▞ ▟
I don't see anything obvious.
So what was the process used to decide their order?