opensimplex 0.2
OpenSimplex ndimensional gradient noise function.
OpenSimplex noise is an ndimensional gradient noise function that was developed in order to overcome the patentrelated issues surrounding Simplex noise, while continuing to also avoid the visuallysignificant 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 hardwareimplementationoptimized 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 “scissorsimplices” 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 scissorsimplex lattice. Simplex Noise divides the (squashed) ndimensional (hyper)cube into n! simplices based on ordered edge traversals, whereas OpenSimplex Noise divides the (stretched) ndimensional (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:
File  Type  Py Version  Uploaded on  Size  

opensimplex0.2.tar.gz (md5)  Source  20160620  13KB  
 Author: A. Svensson
 Home Page: https://github.com/lmas/opensimplex
 Download URL: https://github.com/lmas/opensimplex/releases
 Keywords: opensimplex simplex noise 2D 3D 4D
 License: MIT

Categories
 Development Status :: 4  Beta
 License :: OSI Approved :: MIT License
 Programming Language :: Python :: 2
 Programming Language :: Python :: 2.7
 Programming Language :: Python :: 3
 Programming Language :: Python :: 3.3
 Programming Language :: Python :: 3.4
 Programming Language :: Python :: 3.5
 Programming Language :: Python :: 3.6
 Topic :: Scientific/Engineering :: Mathematics
 Package Index Owner: lmas
 DOAP record: opensimplex0.2.xml