Okay, there are a lot of comparisons between Perlin and Simplex noise to be found on the web. But I really couldn't find one where there was a simple processing time comparison between both for three dimensions, which is what I am mostly interested in. I've read [that popular PDF](http://webstaff.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf) (and even understood most of it - yay!) but I cannot answer the simple question: Which one is faster for 3D, assuming an optimal implementation?

This [stackoverflow question answer](https://stackoverflow.com/questions/6963388/fastest-perlin-like-3d-noise-algorithm) suggests that Simplex is a pretty clear winner for my case. Of course, there are other resources claiming the exact opposite.

However, the general statement seems to be that Perlin noise has a complexity of O(2^N), while Simplex has O(N^2). Which for 3D would mean 8 for Perlin and 9 for Simplex. **But**, on some site I found the statement that Simplex is actually O(N). So what **is** true here, and what does that really mean for speed in 3D?

I am at a loss here, I'm really mainly interested in 3D application (for random terrain generation including caves) usage, and I cannot find a good answer to the question which one I should use if I want it to be as fast as possible.

So maybe someone can help me here :)