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The Simplex Noise (or Improved Perlin Noise) algorithm uses a somewhat mysterious "skew factor" of 3-12. I did not find any really satisfactory explanation for this factor in the descriptions of Simplex Noise that I read. But I managed to work it out nevertheless, which I thought was a fun exercise and worth a quick write-up.
Simplex noise is constructed by assigning random values to each point in a simplex grid. The simplex grid is a tiling of the plane using rhombuses, each rhombus consisting of two equilateral triangles. See the figure on the right.
Given a point (x,y) (expressed in normal rectangular coordinates), we …[Read more]