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How do I create tileable 3D Perlin/Simplex noise?

I have a library which provides functions for 1/2/3/4-D simplex noise. With that I successfuly created a tileable 2D cloud texture (see How do you generate tileable Perlin noise?). Now I want to ...
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Perlin simplex noise transformations

I am programming the simplex noise and I am a bit confusing about about the transformations between simplex and regular grid. I understand it this way: I start in simplex grid. Then I transform input ...
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Simplex noise input problem

I am running simplex noise on a compute shader and am having problems getting an even(ish) distribution, with very obvious errors. I know this is due to particular inputs used but I have no bases for ...