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Perlin noise is a type of gradient noise developed by Ken Perlin in 1983. It has many uses, including but not limited to: procedurally generating terrain , applying pseudo-random changes to a variable, and assisting in the creation of image textures .
Perlin noise is the earliest form of lattice noise, which has become very popular in computer graphics. Perlin Noise is not suited for simulation because it is not divergence-free. Noises based on lattices, such as simulation noise and Perlin noise, are often calculated at different frequencies and summed together to form band-limited fractal ...
Simplex noise. Simplex noise is the result of an n-dimensional noise function comparable to Perlin noise ("classic" noise) but with fewer directional artifacts, in higher dimensions, and a lower computational overhead. Ken Perlin designed the algorithm in 2001 [1] to address the limitations of his classic noise function, especially in higher ...
Abstract composition in 3D generated with the OpenSimplex noise generation algorithm. OpenSimplex noise is an n-dimensional (up to 4D) gradient noise function that was developed in order to overcome the patent-related issues surrounding simplex noise, while likewise avoiding the visually-significant directional artifacts characteristic of Perlin noise.
2) Perlin Noise is not white noise. A single "layer" of Perlin noise (or value noise, or any type of noise, there are many)has only one frequency, not all of them. You much blend together many "layers" of Perlin noise to collaborate various frequencies together in one noise (known as spectral synthesis).
Noise in computer graphics refers to various pseudo-random functions used to create textures, including: Gradient noise, created by interpolation of a lattice of pseudorandom gradients Perlin noise, a type of gradient noise developed in 1983; Simplex noise, a method for constructing an n-dimensional noise function comparable to Perlin noise
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Common techniques include Simplex noise, fractals, or the diamond-square algorithm, which can generate 2-dimensional heightmaps. A version of scenery generator can be very simplistic. Using a diamond-square algorithm with some extra steps involving fractals an algorithm for random generation of terrain can be made with only 120 lines of code.