Touch of 127.5

This is simply the original "thingy" image with a checkerboard half of its pixels negated. Or if the same checkerboard half is instead rotated 180. There is probably some way to make an even grayer image by starting with one whose segment boundaries tend to be higher contrast. But that would be a subtle reduction in only a 1D quantity. As far as goes the 2D bulk, this is about as gray as it gets.