What is the range of a noise over some probability to be calculated?

[SettingDust]

How to calculate the range of a noise?

Context:

@jacobsjo : Calculating the range of a noise is quite tricky, since it can get quite large when all amplitudes happen to add up, but its very rare for the noise to actually get to those values. The range shown by the df editor are what is used internally for density function optimization and is just a very conservative estimate.

https://discord.com/channels/507304429255393322/807617588045545523/1246434297288720385

Off-topic: I couldn't find a trackable place to discuss the world generation issue. Discord can't be indexed on search engines. So I posted a discussion here.

[SettingDust]

https://discord.com/channels/507304429255393322/807617588045545523/1246879516081655960

@itsmiir: i would imagine you could get pretty close by assuming that the values returned by the noise algorithm are normally distributed

I found out I can export the noise image from the canvas on noise generator and generate a histogram for the grayscale image to analyze the distribution. For export, you have to disable the context menu event of the canvas in browser developer tools.
Since we can calculate the actual max value by https://minecraft.wiki/w/Noise. It's possible to match the grayscale and the actual value.
It is indeed an approximately normal distribution