Then I reversed the direction of half the blocks:
Then I changed the direction of the middle line compared to the outer lines (of the block unit):
Then flipped the direction of the blocks again. This one is my favorite (ignoring the limited color palette, of course). And when you look closely at the square unit (in this case, 6x6 of them) you see that it's just two sets of 2 strips that have been cut at a 45 degree angle and sewn back to back, or else you could piece the blocks together from triangles and strips... I'm calling this "Diamond in the Rough", and definitely plan to make it someday:
Then I rotated a small selection of the above so the blocks weren't on point and it makes this super simple quilt (but I don't like it much compared to the visually interesting one above):
I also saw this image of Half-square triangles by Susie Z on Flickr, and you can see all the possibilities of ways to arrange HSTs, so I made a quick mock-up in - you can see all the lights are placed in one direction and the darks in another, which creates the visual effect of squares on point:
This is the selection of fabrics from my stash that I've picked out to work on this quilt:
I narrowed it down to 30 of the above fabrics and cut 7" squares from each for making HSTs to position randomly for a very simple version of the last mock-up in this post - I'll have to make 'Diamond in the Rough' another time, when I have more time to execute it properly.
Here are several arrangements of the HST-squares on the design wall: