Thank you for explaining this better! This is still a bit complicated on the Math side but it’s well illustrated to see the result.

What an impressive and thorough deep dive. I remember first learning about gradient noise through shader examples online, but never realized how much complexity lies beneath the surface. In my own projects, I’ve definitely been guilty of assuming “it looks good enough” without considering all the finer mathematical details. Seeing how derivatives and numerical stability play such a key role really gives me a new appreciation for how much work goes into getting these effects to look smooth and natural. Have any of you ever gotten lost tweaking fade functions to get that perfect wave-like look?

One thing I've been meaning to look into - how to adapt 3D perlin noise to produce gaussian noise - given a specified (scalar) mean and standard deviation.

Why not generate gaussian noise from scratch? By definition it should be indistinguishable.

Pretty and informative!