I finally managed to get a 4D version of Perlin's simplex noise working in GLSL. The simplex ordering was the trickiest part, but the result clearly shines in performance compared to classic 4D noise, which I also implemented for comparison.

Simplex noise is about twice as fast in 4D!

Zip archive with Win32 executable demo and full source

Note that you can test all six flavors of noise (2D, 3D, 4D, classic and simplex) by commenting out and uncommenting lines in main() at the end of the fragment shader file and simply restarting the program.

This is the last update from me for a while, the analytic derivative computation will have to wait. If anyone else feels up to that task, please do it and share the result with the rest of us.