OpenSimplex n-dimensional gradient noise function.

## Project description

OpenSimplex noise is an n-dimensional gradient noise function that was developed in order to overcome the patent-related issues surrounding Simplex noise, while continuing to also avoid the visually-significant directional artifacts characteristic of Perlin noise.

This is merely a python port of Kurt Spencer’s original code, released to the public domain, and neatly wrapped up in a package.

## USAGE

### Initialization:

>>> from opensimplex import OpenSimplex >>> tmp = OpenSimplex() >>> print (tmp.noise2d(x=10, y=10)) 0.732051569572

Optionally, the class accepts a seed value:

>>> tmp = OpenSimplex(seed=1) >>> print (tmp.noise2d(x=10, y=10)) -0.4790979022623557

The seed must be a valid python number. It’s used internally to generate some permutation arrays, which is used for the noise generation.

If it isn’t provided the class will **default to use 0 as the seed**.

### Available class methods:

- OpenSimplex.noise2d(x, y)
- Generate 2D OpenSimplex noise from X,Y coordinates.
- OpenSimplex.noise3d(x, y, z)
- Generate 3D OpenSimplex noise from X,Y,Z coordinates.
- OpenSimplex.noise4d(x, y, z, w)
- Generate 4D OpenSimplex noise from X,Y,Z,W coordinates.

### Running tests and benchmarks:

First make a virtualenv and install the dev. requirements:

virtualenv venv source venv/bin/activate pip install -r requirements.txt

and then simply run the tests:

make test

- or the basic benchmark:
- make benchmark

## FAQ

Is this relevantly different enough to avoid any real trouble with the original patent?

If you read the patent claims:

Claim #1 talks about the hardware-implementation-optimized gradient generator. Most software implementations of Simplex Noise don’t use this anyway, and OpenSimplex Noise certainly doesn’t.

Claim #2(&3&4) talk about using (x’,y’,z’)=(x+s,y+s,z+s) where s=(x+y+z)/3 to transform the input (render space) coordinate onto a simplical grid, with the intention to make all of the “scissor-simplices” approximately regular. OpenSimplex Noise (in 3D) uses s=-(x+y+z)/6 to transform the input point to a point on the Simplectic honeycomb lattice so that the simplices bounding the (hyper)cubes at (0,0,..,0) and (1,1,…,1) work out to be regular. It then mathematically works out that s=(x+y+z)/3 is needed for the inverse transform, but that’s performing a different (and opposite) function.

Claim #5(&6) are specific to the scissor-simplex lattice. Simplex Noise divides the (squashed) n-dimensional (hyper)cube into n! simplices based on ordered edge traversals, whereas OpenSimplex Noise divides the (stretched) n-dimensional (hyper)cube into n polytopes (simplices, rectified simplices, birectified simplices, etc.) based on the separation (hyper)planes at integer values of (x’+y’+z’+…).

Another interesting point is that, if you read all of the claims, none of them appear to apply to the 2D analogue of Simplex noise so long as it uses a gradient generator separate from the one described in claim #1. The skew function in Claim #2 only applies to 3D, and #5 explicitly refers to n>=3.

And none of the patent claims speak about using surflets / “spherically symmetric kernels” to generate the “images with texture that do not have visible grid artifacts,” which is probably the biggest similarity between the two algorithms.

**Kurt**, on Reddit.

## CREDITS

- Kurt Spencer - Original work
- A Svensson - Python port and package author
- CreamyCookie - Cleanup and optimizations

## LICENSE

While the original work was released to the public domain by Kurt, this package is using the MIT license. Please see the file LICENSE for details.

## Expected Output

2D noise (with default seed):

3D noise:

4D noise:

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