I’ve been thinking about the possibilities of double plain weave with a white/black alternation in both warp and weft.
Here is a schematic. The warp and weft colors are indicated along the top and left. Yellow indicates light or white warp and weft, and red indicates dark or black warp and weft. The black and white squares are the actual weave structure: black indicates warp up. The weave in this example is #1, white warp and white weft on top.
The layer which appears on the face of the cloth could be:
1. All white (white warp and white weft on top)
2. All black (black warp and black weft on top)
3. Gray toned (white warp and black weft on top)
4. Gray toned (black warp and white weft on top)
5. White with black speckles (white warp, black and white wefts on top)
6. Black with white speckles (black warp, black and white wefts on top)
7. White with black speckles (white and black warp, white weft on top)
8. Black with white speckles (white and black warp, black weft on top)
Examples #3 and #4 would appear the same when woven. Likewise #5 and #7; likewise #6 and #8.
Here are the eight examples, reading from left to right (the green squares are separators).
You could use these weaves as pattern presets for jacquard design in Photoshop, or paste them into your dobby lift plans with a straight threading.