Started really late tonight. This is definitely one of the "open up the computer, see where it goes!" projects.
Part A is a "reducing checkerboard" tile. Row 1's squares descend at a rate of 1 - 1/8 = 7/8 = 87.5%. Row 2's squares descend at a rate of 1 - 2/8 = 6/8 = 75%, and so on, where the (very simple) reduction formula is (8-n)/8 where n is the row number.
Part B is a compilation of these tiles. Column 1 is patterned down in 180 degree flips. Each row is seeded by the Column 1 tile and is patterned with 90 degree rotations. Interesting patterns came out of this.