random number generator with x,y coordinates as seed

Question

I'm looking for a efficient, uniformly distributed PRNG, that generates one random integer for any whole number point in the plain with coordinates x and y as input to the function.

int rand(int x, int y)

It has to deliver the same random number each time you input the same coordinate.

Do you know of algorithms, that can be used for this kind of problem and also in higher dimensions?

I already tried to use normal PRNGs like a LFSR and merged the x,y coordinates together to use it as a seed value. Something like this.

int seed = x << 16 | (y & 0xFFFF)

The obvious problem with this method is that the seed is not iterated over multiple times but is initialized again for every x,y-point. This results in very ugly non random patterns if you visualize the results.

I already know of the method which uses shuffled permutation tables of some size like 256 and you get a random integer out of it like this.

int r = P[x + P[y & 255] & 255];

But I don't want to use this method because of the very limited range, restricted period length and high memory consumption.

Thanks for any helpful suggestions!

Answer 1

I found a very simple, fast and sufficient hash function based on the xxhash algorithm.

// cash stands for chaos hash :D
int cash(int x, int y){   
    int h = seed + x*374761393 + y*668265263; //all constants are prime
    h = (h^(h >> 13))*1274126177;
    return h^(h >> 16);
}

It is now much faster than the lookup table method I described above and it looks equally random. I don't know if the random properties are good compared to xxhash but as long as it looks random to the eye it's a fair solution for my purpose.

This is what it looks like with the pixel coordinates as input: