OpenSimplex noise

OpenSimplex noise is an n-dimensional gradient noise function that was developed in order to overcome the patent-related issues surrounding Simplex noise, while continuing to also avoid the visually-significant directional artifacts characteristic of Perlin noise.

The algorithm shares numerous similarities with Simplex noise, but has two primary differences:

• Whereas Simplex noise starts with a Hypercubic honeycomb and squashes it down the main diagonal in order to form its grid structure,[1] OpenSimplex noise instead swaps the skew and inverse-skew factors and uses a stretched hypercubic honeycomb. The stretched hypercubic honeycomb becomes a Simplectic honeycomb after subdivision.[2] This means that 2D Simplex and 2D OpenSimplex both use different orientations of the Triangular tiling, but whereas 3D Simplex uses the Tetragonal disphenoid honeycomb, 3D OpenSimplex uses the Tetrahedral-octahedral honeycomb.[2]
• OpenSimplex noise uses a larger kernel size than Simplex noise. The result is a smoother appearance at the cost of performance, as additional vertices need to be determined and factored into each evaluation.[2]