Earlier quoted context omitted.
As a physicist who works with quantum mechanics, I have to say, "wave function collapse", is an extremely apt name for what you're describing. Usually when quantumy things are used in names of things it's just 'cause it sounds cool, but this is spot-on.
It's really not. There's no probability field (unless you count booleans as a scalar), no complex numbers, and no entanglement. It's just constraint propogation, optimized for certain conditions and given a fancy name. I guess you could call it a markov random field, but I don't think it does unbiased sampling.
1) X ? 2) X Y 3) X ? 4) X Y
? ? ? ? Z ? Z ?
The probability of some particular tile in the bottom right corner may be bigger in 2) and 3) because somehow Y and Z make this tile more probable, but perhaps in 4) the probability decrease.The trick is that you must calculate amplitudes, not probabilities. For example, Y may contribute an amplitude of .5 to the bottom right corner , and the probability is (.5)^2=.25. And Z may contribute an amplitude of -.3 to the bottom right corner , and the probability is (-.3)^2=.09. But when both are there the amplitudes must be added and the probability is (.5-.3)^2=.04.
This is a case of destructive interference that reduces the probability of a particular tile when both are present, but if both have the same sign it can be a constructive interference and increase the probability of that tile.
This type of interference is what produce the weird interference lines in the double slit experiment (and even in the single slit experiment).
This project just add probabilities, without squaring the numbers, so it's more difficult to have quantum-like weird things.
Anyway, I like the result very much. Nice project. Nice name.