Perlin noise

Perlin noise is a type of gradient noise developed by Ken Perlin in 1983 as a result of his frustration with the 'machine-like' look of computer graphics at the time. He formally described his findings in a SIGGRAPH paper in 1985 called An image Synthesizer. In 1997, Perlin was awarded an Academy Award for Technical Achievement for creating the algorithm:To Ken Perlin for the development of Perlin Noise, a technique used to produce natural appearing textures on computer generated surfaces for motion picture visual effects. Perlin noise is a type of gradient noise developed by Ken Perlin in 1983 as a result of his frustration with the 'machine-like' look of computer graphics at the time. He formally described his findings in a SIGGRAPH paper in 1985 called An image Synthesizer. In 1997, Perlin was awarded an Academy Award for Technical Achievement for creating the algorithm: Perlin did not apply for any patents on the algorithm, but in 2001 he was granted a patent for the use of 3D+ implementations of simplex noise for texture synthesis. Simplex noise has the same purpose, but uses a simpler space-filling grid. Simplex noise alleviates some of the problems with Perlin's 'classic noise', among them computational complexity and visually-significant directional artifacts. Perlin noise is a procedural texture primitive, a type of gradient noise used by visual effects artists to increase the appearance of realism in computer graphics. The function has a pseudo-random appearance, yet all of its visual details are the same size. This property allows it to be readily controllable; multiple scaled copies of Perlin noise can be inserted into mathematical expressions to create a great variety of procedural textures. Synthetic textures using Perlin noise are often used in CGI to make computer-generated visual elements – such as object surfaces, fire, smoke, or clouds – appear more natural, by imitating the controlled random appearance of textures in nature. It is also frequently used to generate textures when memory is extremely limited, such as in demos, and is increasingly finding use in graphics processing units for real-time graphics in computer games. Perlin noise resulted from the work of Ken Perlin, who developed it at Mathematical Applications Group, Inc. (MAGI) for Disney's computer animated sci-fi motion picture Tron (1982). In 1997, he won an Academy Award for Technical Achievement from the Academy of Motion Picture Arts and Sciences for this contribution to CGI. Perlin noise is most commonly implemented as a two-, three- or four-dimensional function, but can be defined for any number of dimensions. An implementation typically involves three steps: grid definition with random gradient vectors, computation of the dot product between the distance-gradient vectors and interpolation between these values. Define an n-dimensional grid where each point has a random n-dimensional unit-length gradient vector, except in the one dimensional case where the gradients are random scalars between -1 and 1. Assigning the random gradients in one and two dimensions is trivial using a random number generator. For higher dimensions a Monte Carlo approach can be used where random Cartesian coordinates are chosen in a unit cube, points falling outside the unit ball are discarded, and the remaining points are normalized to lie on the unit sphere. The process is continued until the required number of random gradients are obtained. In order to negate the expensive process of computing new gradients for each grid node, some implementations use a hash and lookup table for a finite number of precomputed gradient vectors. The use of a hash also permits the inclusion of a random seed where multiple instances of Perlin noise are required.