How can Perlin Noise be modified to not tile?

Question

In vanilla perlin noise, the texture repeats after 256 coordinates, due to the way it picks a gradient vector. In games that require an infinite procedural world, however, this is not an acceptable tradeoff. This requires a different method to pick the gradient vector. I need an alternative that is portable in C++, meaning that I will get the same noise for the same seed on different systems.

I have come across two options to do this:

• Using C++'s random api, using bitshift-modified coordinates as the seed, but this is very slow in practice and is too reliant on the exact implementations of the C++ random number generators, which may or may not guarantee the same sequence of numbers across platforms.
• Use a much faster random hash function I found in the old freespace virgin "perlin noise" (actually value noiswe) tutorial, which I saved before it went down. The issue with this one is that it has bitshift on signed integers, and thus has undefined behaviour in C++.

EDIT: Something I forgot to mention in the original question is that I need to be able to re-seed the perlin noise engine to get a different output. With vanilla perlin noise, I can simply use a seeded random shuffle on the hash table lookup array before calculating anything else.

Answer 1

It sounds like you already know the solution to your problem: replace the initial 256-entry table lookup with a hash/digest of the whole coordinate value, not just the low 8 bits.

From there the only question that remains is which hash function to use, and there are tons out there that you can try on for size if the one in the tutorial didn't meet your needs.

The issue with this one is that it has bitshift on signed integers, and thus has undefined behaviour in C++.

Note too that even if your coordinates represent signed positions in your game world or texture space, Perlin noise doesn't need to know that. All it cares about is reproducibly selecting different gradient vectors for each distinct set of integer inputs, so you can re-interpret the bit patterns as unsigned integers and it's still just as happy.

Answer 2

The original definition of Perlin noise doesn't mention a fixed size permutation table. That's only a speed improvement, because generating pseudo random values based on coordinates is usually a slow or complicated process.

Stefan Gustavson solved this issue in his glsl implementation by using a function. As stated here this won't make it infinitely long either, but you can pick a prime number large enough for your needs. For instance, using 9997643 and 9997237 would put the first repetition at 99948806512391, but make sure your data types can handle division by those values nicely.

Another approach is to use a seeded random generator. Create a unique number from the coordinates (for instance if you use two 32 bit integers for coordinates, then just do x << 32 | y to get a unique 64 bit number), set it as the seed of the random function and generate a value. That should be the same every time you query that position.