Tiling Simplex Noise?

Question

I've been interested (as a hobbyist) in pseudo-random noise generation, specifically the Perlin and Simplex algorithms. The advantage to Simplex is speed (especially at higher dimensions), but Perlin can be tiled relatively easily. I was wondering if anyone was aware of a tiling simplex algorithm? Fixed-dimension is fine, generic is better; pseudocode is fine, c/c++ is better.

Answer 1

I had the same question in mind some time back. This link may help you a bit.

http://www.gamedev.net/community/forums/topic.asp?topic%5Fid=409855

Answer 2

I recently needed tiling simplex noise and came across this question.

For tiling noise using any noise function, you can linearly interpolate additional tile samples:

Ftileable(x, y) = ( 
       F(x, y) * (w - x) * (h - y) + 
       F(x - w, y) * (x) * (h - y) + 
       F(x - w, y - h) * (x) * (y) + 
       F(x, y - h) * (w - x) * (y)
) / (wh)

where F() is your noise function. Note that x, y must be coordinates within an individual tile: x in [0, w), y in [0, h). You could use something like tileX = x - Math.Floor(x / w) * w or fmod().

If performance is critical or for higher dimensions, this may not be the way to go because it requires 2^D lookups for dimension D. It also produced lower values toward the centers of tiles for me.

Taken from: http://webstaff.itn.liu.se/~stegu/TNM022-2005/perlinnoiselinks/perlin-noise-math-faq.html