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:

Whereas classical noise interpolates between the gradients at the surrounding hypergrid end points (i.e., northeast, northwest, southeast and southwest in 2D), simplex noise divides the space into simplices (i.e., ${\displaystyle n}$-dimensional triangles). This reduces the number of data points. While a hypercube in ${\displaystyle n}$ dimensions has ${\displaystyle 2^{n}}$ corners, a simplex in ${\displaystyle n}$ dimensions has only ${\displaystyle n+1}$ corners. The triangles are equilateral in 2D, but in higher dimensions the simplices are only approximately regular. For example, the tiling in the 3D case of the function is an orientation of the tetragonal disphenoid honeycomb.

...
Wikipedia