Simplex noise
Ken Perlin's 2001 redesign of his own gradient noise, built on a simplex grid that scales better to high dimensions and shows fewer axis-aligned artifacts.
Perlin noise (1983) samples a cubic lattice, which means 2ⁿ corners per point — eight in 3D, sixteen in 4D. Simplex noise swaps the cube for the simplest space-filling shape: a triangle in 2D, a tetrahedron in 3D. That needs only n+1 corners, the cost grows as O(n²) instead of O(2ⁿ), and the gradients are well defined, free of the grid-aligned banding that plagues the older noise.
Perlin presented it at SIGGRAPH 2001. That the algorithm was patented spawned the patent-free clone OpenSimplex (2014), which many engines adopted to sidestep the question. It is used for terrain, clouds and procedural textures, usually summed in octaves for fractal detail. Its relatives value noise and Worley noise solve the same problem by other means.