Simplex noise
Simplex noise is a method for constructing an n-dimensional noise function comparable to Perlin noise ("classic" noise) but with fewer directional artifacts and, in higher dimensions, a lower computational overhead. Ken Perlin designed the algorithm in 2001 to address the limitations of his classic noise function, especially in higher dimensions.
The advantages of simplex noise over Perlin noise:
Simplex noise has a lower computational complexity and requires fewer multiplications.
Simplex noise scales to higher dimensions (4D, 5D) with much less computational cost, the complexity is
for
dimensions instead of the
of classic noise.
Simplex noise has no noticeable directional artifacts (is visually isotropic), though noise generated for different dimensions are visually distinct (e.g. 2D noise has a different look than slices of 3D noise, and it looks increasingly worse for higher dimensions).
Simplex noise has a well-defined and continuous gradient (almost) everywhere that can be computed quite cheaply.