stegu/webgl-noise is a repository of GLSL shaders implementing Simplex, Perlin, and Worley noise.
Compare 2D Simplex noise with 2D Perlin noise:
3D Simplex and Perlin noise on a sphere:
The obvious visual differences between Simplex noise (left) and Perlin noise (right) disappear when many octaves are added using fractal Brownian motion (fBm). These are 2D slices through 3D noise:
These are 3D slices through 4D noise:
Click on an image to generate a shadertoy-compatible shader: