December 9, 1999 - Ken Perlin
This article is written by the man who fathered perlin noise. It begins with the history of the noise and ends with a detailed explanation of how to generate the noise. It can however be a little difficult to decipher exactly what he means since he doesn't use any figures to demonstrate his formulas.
Jan, 1998 - Makoto Matsumoto, Takuji Nishimura
Compared to the standard implementation of rand() the MT can be made 4 times faster and are many times better, meaning higher degree of randomness and longer period for the returned numbers. The algorithm is free to use commercially.
This article explains how to create and use perlin noise. Actually, this probably isn't real perlin noise, as in how Ken Perlin did it, but the result looks very similar.
The perlin noise math FAQ
February 2001 - Matt Zucker
This FAQ explains very well what perlin noise is and how to generate it. It also explains how to make it tileable.
2002 - Ken Perlin
This article describes how to improve the looks and efficiency of the original Perlin Noise function by choosing a special set of gradient vectors that allow for removal of mathematical operations, and also choosing a better interpolation function.
Generating Perlin Noise
February, 2002 - Andreas Jönsson
Describes the original perlin noise algorithm, complete with sample source code.
Ken Perlin's homepage
ISAAC: a fast cryptographic random number generator
A fast random number generator
Simplex noise demystified
Mar, 2005 - Stefan Gustavson
This article explains how the simplex noise algorithm works. Simplex noise is the second noise algorithm that Ken Perlin invented, and is an improvement over the previous perlin noise algoritm, both in terms of performance and visual quality.
Agner Fog's home page
This site has valuable information on software optimizations, and also a few other cool stuff, such as random number generators, CPU detection routines, and links to other resources.