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WFC is a full method of map generation. Monte Carlo is not afaik.
Edit: To answer your question, the original paper on WFC uses training data, hyperparameters, etc. They took a grid of pixels (training data), scanned it using a kernal of varying size (model parameter), and used that as the basis for the wavefunction probability model. I wouldn't call it AI though because it doesn't train or self-improve like ML does.
I think the training (or fitting) process is comparable to how a support vector machine is trained. It's not iterative like SGD in deep learning, it's closer to the traditional machine learning techniques.
But I agree that this is a pretty academic discussion, it doesn't matter much in practice.
MC is a statistical method, it doesn't have anything to do with map generation. If you apply it to map generation, you get a "full method of map generation", and as far as I know that is what WFC is.
Could you share the paper? Everything I read about WFC is "you have tiles that are stitched together according to rules with a bit of randomness", which is literally MC.
Ok so you are just talking about MC the statistical method. That doesn't really make sense to me. Every random method will need to "roll the dice" and choose a random outcome like a MC simulation. The statement "this method of map generation is the same as Monte Carlo" (or anything similar, ik you didn't say that exactly) is meaningless as far as I can tell. With that out of the way, WFC and every other random map generation method are either trivially MC (it randomly chooses results) or trivially not MC (it does anything more than that).
The original Github repo, with examples of how the rules are generated from a "training set": https://github.com/mxgmn/WaveFunctionCollapse A paper referencing this repo as "the original WFC algorithm" (ref. 22): long google link to a PDF
Note that I don't think the comparison to AI is particularly useful-- only technically correct that they share some similarities.
I don't think WFC can be described as an example of a Monte Carlo method.
In a Monte Carlo experiment, you use randomness to approximate a solution, for example to solve an integral where you don't have a closed form. The more you sample, the more accurate the result.
In WFC, the number of random experiments depends on your map size and is not variable.
Sorry, I should have been more specific - it's an application of Markov Chain Monte Carlo. You define a chain and randomly evaluate it until you're done - is there anything beyond this in WFC?
I'm not an expert on Monte Carlo methods, but reading the Wikipedia article on Markov Chain Monte Carlo, this doesn't fit what WFC does for the reasons I mentioned above. In MCMC, your get a better result by taking more steps, in WFC, the number of steps is given by the map size, it can't be changed.
I'm not talking about repeated application of MCMC, just a single round. In this single round, the number of steps is also given by the map size.