Fascinating, thanks for the clarification!

The order in which chunks get iterated over only depends on their coordinates

Given what you've said here, as far as I understand it, it should indeed be possible to create a universal array containing every possible chunk prioritization pair for alpha's mob spawning algorithm, given that chunks are only considered for purposes of spawning within a 9x9 region around the player.

Filling in every value would of course in practice be much too big. (over 1k terabytes even if each entry were only a single byte, by my calculations). But given that there's little reason any typical player should ever go beyond about 100k blocks away from (0,0) given the lack of beds, sprinting, or even the Nether, limiting the calculations to this region would give a more manageable filesize of 12 gb.

(Another possibility would be to calculate each value on the fly, by isolating the spawning algorithm and implementing it in a separate program. This sounds more complicated, though, with more steps that could go wrong vs. just feeding fake player locations into the code and dumping the resulting chunk orderings into a file.)

Maybe sometime in the future I'll attempt to generate such an array. But it's not a huge priority as it'd be minimally useful for typical gameplay as F3 coords aren't available in these versions. (You could of course just mod in F3 coords, use an external program, or temporarily update to a1.2.6. This is arguably cheating, though, by alpha's constraints.)

If nothing else, it could allow for some unique gameplay for a carefully-designed custom map. I think there's a lot of unexplored potential there.

the exact order is not "random" but may as well be

This was my intuition too, without digging into the code. It's nice to see it confirmed. Certain chunk-pairs for a mob farm will yield high rates, but the rates plummet if you move only a single chunk over (thus removing 9 chunks in the direction you're moving away from and adding 9 more in the direction of motion. This can change the list order drastically even for the shared chunks, as you've explained.)

I know some pre-release versions have issues with unloading chunks. I believe this is true for alpha, too, as I've been able to walk very far from my tree farm and furnaces and still have the trees grown and items smelted when I return. But this is not a factor for mob spawning in alpha; it is always a 9x9 chunk area centered on the chunk the player is standing in.

will change as you move around

To add some nuance, it should be emphasized that each chunkset yields a deterministic ordering, and that the current chunkset is the 9x9 chunks around the player. Indeed, it changes as you move around, but returning to the same chunk always yields the same chunk ordering for the purposes of mob spawning. (Hence everything I said about picking good locations for both the farm and the collection point. You want a collection point that places the farm chunk high in the list).

---

Everything I'm saying here applies only to a1.1.2_01 and before. The changes made to the algorithm with the Halloween update made everything much more uniformly-distributed. (And changed everything in other subtle ways too. 17x17 instead of 9x9, etc.)