Back on topic, even if the tiler just relied on the random function as pulling the different tiles out of the box in a random order, the tile job would still be pseudo random as the truly random pattern would only appear randomly. If there were a different tiler for every tile, it might be more random.
Just for the hell of it, I'm going to post some philosophical ideas about randomness.
The way I see it is that "random" can be thought of as meaning "uncorrelated to
stuff". Truly perfectly flawlessly random would mean "uncorrelated to anything else in the universe". That's one possible definition for randomness.
For tiling using a pseudo random number generator, the tile pattern would end up being correlated to the output of the PRNG, but I don't think that correlation would be of any significance to anybody, and so I'd still call it random.
Now, here's a kicker, some people might like to suggest that the tile placement would be random if it was based on the nuclear decay of some radioactive isotope, or some other quantum mechanical effect which is known to be truly random... Well, let me put this to you: if the tile placement was determined by this random nuclear decay, then it still wouldn't be
truly perfectly flawlessly random because it would be correlated to the nuclear decay!
The nuclear decay cannot be predicted in advance, but the tile placement can be predicted by anyone else who happens to be watching the same nuclear decays. So in the time between the truly random input (the nuclear decay) and the tiles actually being placed, there is nothing random about the placement at all. It's completely predetermined. The tiles are not placed, but you know exactly where they are going to go. So it is not
truly perfectly flawlessly random. It is, however, only correlated with some stuff which probably has no other practical significance, and cannot be predicted, and so on - so for all intents and purposes I think it's fair enough to call it random... just not in the very strictest sense.
Another possible definition of "random" is that true randomness cannot be predicted in advance. So if something is
truly perfectly flawlessly random, that would mean not even an omniscience god would be able to predict the outcome of the randomness. Again, various quantum mechanical effects would match this definition, but basically nothing else would. However, since I think we can assume there are no omniscience gods among us, we can settle for just basing our randomness on stuff which is very difficult to know. For example, for basic needs, flipping a coin is good enough to be 'random'. Maybe the outcome could be predicted if we knew exactly how hard the coin would be struck, and how the air was behaving around the coin and so on; but since we don't know those things, the coin flip can be thought of as random. For more serious randomness used, for example, to generate secure cryptographic keys for money transactions and whatnot we typically settle for things like the precise fraction of a second at which network signals reach our computer, or at which keys are struck, and so on. (
here is a link describing what I'm talking about.) By using a bunch of
difficult to know things, and mashing them up together into a big soup which could only be predicted by someone who knows
all of the
difficult to know stuff; we are able to generate a sequence of number which are unpredictable. The sequence still isn't
truly perfectly flawlessly random, because an omniscience being could still predict the sequence, but that stuff is random enough for us to trust it with our life's savings! (As I said, money transactions over the internet rely on this kind of thing.)
Again, with the tiler using the nuclear decay random source thing; if you think of the nuclear decay source as part of the process of tiling, then I suppose you could say it was completely random because it is is completely unpredictable - but if you do not think of them as separate events, then the tiling is not random, because anyone who views the nuclear decays would then be able to predict the sequence used in the tiling.
The bottom line is that
truly perfect flawless randomness is extremely rare; because it's pretty difficult to hide stuff from an omniscience being... But to hide information from humans is not hard, and so we can effectively get randomness just by flipping a coin, or using a pseudo random number generator - and that 'pseudo' randomness is completely indistinguishable from
truly perfect flawless randomness as long as we are unable to determine the required information.
By the way, games are usually programmed so that the 'required information' that the PRNG is based on is deliberately
not secret, because they like to be able to reproduce the same sequence of 'random' numbers for save games, or for multiplayer network games, and so on. ie. in many games, true randomness is actually not something we want.
[* By the way, I've not studied the philosophy of randomness or anything like that. But I do know a fair bit about quantum mechanics and mathematics... and I've basically just made up these definitions and thoughts based on that knowledge. Let me know if you think I'm off the mark.]
). Besides, a computer can only approximate a random number, but it does a fairly good job.
