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**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.

The algorithm shares numerous similarities with simplex noise, but has two primary differences:

- Whereas simplex noise starts with a hypercubic honeycomb and squashes it down the main diagonal in order to form its grid structure,
^{ [1] }OpenSimplex noise instead swaps the skew and inverse-skew factors and uses a stretched hypercubic honeycomb. The stretched hypercubic honeycomb becomes a simplectic honeycomb after subdivision.^{ [2] }This means that 2D Simplex and 2D OpenSimplex both use different orientations of the triangular tiling, but whereas 3D Simplex uses the tetragonal disphenoid honeycomb, 3D OpenSimplex uses the tetrahedral-octahedral honeycomb.^{ [2] } - OpenSimplex noise uses a larger kernel size than simplex noise. The result is a smoother appearance at the cost of performance, as additional vertices need to be determined and factored into each evaluation.
^{ [2] }

OpenSimplex has a variant called "SuperSimplex" (or OpenSimplex2S), which is visually smoother. "OpenSimplex2F" is identical to the original SuperSimplex.

**Perlin noise** is a type of gradient noise developed by Ken Perlin.

The **Canny edge detector** is an edge detection operator that uses a multi-stage algorithm to detect a wide range of edges in images. It was developed by John F. Canny in 1986. Canny also produced a *computational theory of edge detection* explaining why the technique works.

In computing, **procedural generation** is a method of creating data algorithmically as opposed to manually, typically through a combination of human-generated assets and algorithms coupled with computer-generated randomness and processing power. In computer graphics, it is commonly used to create textures and 3D models. In video games, it is used to automatically create large amounts of content in a game. Depending on the implementation, advantages of procedural generation can include smaller file sizes, larger amounts of content, and randomness for less predictable gameplay. Procedural generation is a branch of media synthesis.

The **Nelder–Mead method** is a commonly applied numerical method used to find the minimum or maximum of an objective function in a multidimensional space. It is a *direct search method* and is often applied to nonlinear optimization problems for which derivatives may not be known. However, the Nelder–Mead technique is a heuristic search method that can converge to non-stationary points on problems that can be solved by alternative methods.

The **tetrahedral-octahedral honeycomb**, **alternated cubic honeycomb** is a quasiregular space-filling tessellation in Euclidean 3-space. It is composed of alternating regular octahedra and tetrahedra in a ratio of 1:2.

The **plasma effect** is a computer-based visual effect animated in real-time. It uses cycles of changing colours warped in various ways to give an illusion of liquid, organic movement.

**Simplex noise** is a method for constructing an *n*-dimensional noise function comparable to Perlin noise but with fewer directional artifacts and, in higher dimensions, a lower computational overhead. Ken Perlin designed the algorithm in 2001 to address the limitations of his classic noise function, especially in higher dimensions.

In seven-dimensional geometry, a **7-polytope** is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets.

In ten-dimensional geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting at each 8-polytope ridge.

**Value noise** is a type of noise commonly used as a procedural texture primitive in computer graphics. It is conceptually different from, and often confused with gradient noise, examples of which are Perlin noise and Simplex noise. This method consists of the creation of a lattice of points which are assigned random values. The noise function then returns the interpolated number based on the values of the surrounding lattice points.

**Gradient noise** is a type of noise commonly used as a procedural texture primitive in computer graphics. It is conceptually different, and often confused with value noise. This method consists of a creation of a lattice of random gradients, dot products of which are then interpolated to obtain values in between the lattices. An artifact of some implementations of this noise is that the returned value at the lattice points is 0. Unlike the value noise, gradient noise has more energy in the high frequencies.

In four-dimensional Euclidean geometry, the **4-simplex honeycomb**, **5-cell honeycomb** or **pentachoric-dispentachoric honeycomb** is a space-filling tessellation honeycomb. It is composed of 5-cells and rectified 5-cells facets in a ratio of 1:1.

In geometry an **omnitruncated simplectic honeycomb** or **omnitruncated n-simplex honeycomb** is an n-dimensional uniform tessellation, based on the symmetry of the affine Coxeter group. Each is composed of omnitruncated simplex facets. The vertex figure for each is an irregular n-simplex.

In six-dimensional Euclidean geometry, the **6-simplex honeycomb** is a space-filling tessellation. The tessellation fills space by 6-simplex, rectified 6-simplex, and birectified 6-simplex facets. These facet types occur in proportions of 1:1:1 respectively in the whole honeycomb.

In geometry, the **simplectic honeycomb** is a dimensional infinite series of honeycombs, based on the affine Coxeter group symmetry. It is given a Schläfli symbol {3^{[n+1]}}, and is represented by a Coxeter-Dynkin diagram as a cyclic graph of *n+1* nodes with one node ringed. It is composed of n-simplex facets, along with all rectified n-simplices. It can be thought of as an n-dimensional hypercubic honeycomb that has been subdivided along all hyperplanes , then stretched along its main diagonal until the simplices on the ends of the hypercubes become regular. The vertex figure of an *n-simplex honeycomb* is an expanded n-simplex.

In geometry, the **cyclotruncated simplectic honeycomb** is a dimensional infinite series of honeycombs, based on the symmetry of the affine Coxeter group. It is given a Schläfli symbol t_{0,1}{3^{[n+1]}}, and is represented by a Coxeter-Dynkin diagram as a cyclic graph of *n+1* nodes with two adjacent nodes ringed. It is composed of n-simplex facets, along with all truncated n-simplices.

In eighth-dimensional Euclidean geometry, the **8-simplex honeycomb** is a space-filling tessellation. The tessellation fills space by 8-simplex, rectified 8-simplex, birectified 8-simplex, and trirectified 8-simplex facets. These facet types occur in proportions of 1:1:1:1 respectively in the whole honeycomb.

In geometry, the **quarter hypercubic honeycomb** is a dimensional infinite series of honeycombs, based on the hypercube honeycomb. It is given a Schläfli symbol q{4,3...3,4} or Coxeter symbol qδ_{4} representing the regular form with three quarters of the vertices removed and containing the symmetry of Coxeter group for n ≥ 5, with = and for quarter n-cubic honeycombs = .

**Noise** refers to many types of random or unwanted signals, most commonly **acoustic noise**, but also including the following:

- Blog post introducing OpenSimplex noise
- Author's current implementation (OpenSimplex2)

- Android library
- C implementation
- GPU implementation in OpenCL
- Heavily-optimized implementation in C#
- Noise library for the Rust programming language providing OpenSimplex noise – does not hard code gradient initial values

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Images, videos and audio are available under their respective licenses.