It seems pretty consistent -- that's probably a Good Thing(tm) in terms of tracking down a cause.
Occasionally prone to off the wall blue skies speculation, I find what's left of my mind wondering about a few things ...
1) The camera itself -- Totally homemade? Modified regular camera? Pinhole to lens distance vs pinhole diameter? Has it ever worked or is this the 1st try?
2) The pinhole -- Homemade? If so, how? or purchased?
3) Film? paper? Loading camera? Developing and handling? Are these prints or inverted scans?
What attempts to pass for reasoning ...
1) A homemade (and maybe even a modified regular camera), especially if it's trying to cover a wide angle, might have stray "junk" interfering with the optical path. That may not be happening here as I would expect obstructions to be sharper in a pinhole scenario. Reflections, as Jim suggests are quite possible. If the attempted angle of view is very wide, it's possible for miscellaneous parts of the camera -- even mounting brackets or shutter flaps -- lifted corners of pieces of tape -- to cause a vignette effect or bounce some light around.
2) A very rough and ragged pinhole, such a one might get by just pushing a pin through foil might cause some odd distortions. Although I'd say these look a little too clean and regular to make that likely. A pinhole in very thick material would tend to increase light fall-off away from the center, though the sky area in those shots looks pretty evenly exposed.
3) In handling, there could be patterns exposed by various light leaks or the like. If doing prints, that offers an additional opportunity for something to sneak in; e.g. dark areas could be light struck paper in the printing and developing process.
I'd say in general the consistency seems to make the typically random effects of some of my speculations unlikely. You might try a shot of a uniformly illuminated light colored wall and see if there's more pattern detail that is recognizable. You might develop a piece of paper/film that has not been exposed to check some issues. That could be expanded to never loaded in the camera, versus loaded in the camera, camera parked in light, but no exposure made.
It's one of those "there's gotta be an explanation" things, but it strikes me as a bit inobvious to track down!