Range of perlin noise

[NielsPichon]

Hi Keijiro,

Thanks for the nice implementation.

I saw your comment regarding the range of the noise in the README, and thought thatb this blogpost may be of interest https://digitalfreepen.com/2017/06/20/range-perlin-noise.html.

There isn't any answer regarding fbm though in the blog post. However in your implementation each subsequent octave has a factor of 0.5^n in front of it. This is actually a known infinite series: we know that for any |x| < 1, Sum_n(x^n) converges to 1 / (1 -x) which in this case is 1 / (1 - 0.5) = 2. So for a fbm with infinitly many octaves, we'd have a maximum bound which is at most 2 * sqrt(N / 4) where N is the dimensionality of the Noise. Whether there is a way to find a stricter bound I am not sure.

I hope you find this interesting.

All the best

[keijiro]

Thanks for the information! I'll update the README based on it.