opensimplex 0.4.5.1
OpenSimplex is a noise generation function like Perlin or Simplex noise, but better.
License: MIT
Requires Python: >=3.8
Keywords: opensimplex simplex noise 2D 3D 4D


# OpenSimplex Noise

[![pypi-version](https://img.shields.io/pypi/v/opensimplex?label=Version)](https://pypi.org/project/opensimplex/)
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[OpenSimplex] is a noise generation function like [Perlin] or [Simplex] noise, but better.

    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.
    - Kurt Spencer

This is merely a python port of Kurt Spencer's [original code] (released to the public domain)
and neatly wrapped up in a package.

[OpenSimplex]: https://en.wikipedia.org/wiki/OpenSimplex_noise
[Perlin]: https://en.wikipedia.org/wiki/Perlin_noise
[Simplex]: https://en.wikipedia.org/wiki/Simplex_noise
[original code]: https://gist.github.com/KdotJPG/b1270127455a94ac5d19

## Status

The `master` branch contains the latest code (possibly unstable),
please refer to the [version tags] for the latest stable version.
An old, archived copy can be found at [Github].

[version tags]: https://code.larus.se/lmas/opensimplex/tags
[Github]: https://github.com/lmas/opensimplex


Updates for **v0.4.***:

- Adds a hard dependency on 'Numpy', for array optimizations aimed at heavier workloads.
- Adds optional dependency on 'Numba', for further speed optimizations using caching
  (currently untested due to issues with llvmlite).
- Adds typing support.
- General refactor and cleanup of the library, tests and docs.
- **Breaking changes: API functions uses new names.**

## Contributions

Bug reports, bug fixes and other issues with existing features of the library are welcomed and will be handled during
the maintainer's free time. New stand-alone examples are also accepted.

However, pull requests with new features for the core internals will not be accepted as it eats up too much weekend
time, which I would rather spend on library stability instead.

## Usage

**Installation**

    pip install opensimplex

**Basic usage**

    >>> import opensimplex
    >>> opensimplex.seed(1234)
    >>> n = opensimplex.noise2(x=10, y=10)
    >>> print(n)
    0.580279369186297

**Running tests and benchmarks**

Setup a development environment:

    make dev
    source devenv/bin/activate
    make deps

And then run the tests:

    make test

Or the benchmarks:

    make benchmark

For more advanced examples, see the files in the [tests](./tests/) and [examples](./examples/) directories.

## API

**opensimplex.seed(seed)**

    Seeds the underlying permutation array (which produces different outputs),
    using a 64-bit integer number.
    If no value is provided, a static default will be used instead.

    seed(13)

**random_seed()**

    Works just like seed(), except it uses the system time (in ns) as a seed value.
    Not guaranteed to be random so use at your own risk.

    random_seed()

**get_seed()**

    Return the value used to seed the initial state.
    :return: seed as integer

    >>> get_seed()
    3

**opensimplex.noise2(x, y)**

    Generate 2D OpenSimplex noise from X,Y coordinates.
    :param x: x coordinate as float
    :param y: y coordinate as float
    :return:  generated 2D noise as float, between -1.0 and 1.0

    >>> noise2(0.5, 0.5)
    -0.43906247097569345

**opensimplex.noise2array(x, y)**

    Generates 2D OpenSimplex noise using Numpy arrays for increased performance.
    :param x: numpy array of x-coords
    :param y: numpy array of y-coords
    :return:  2D numpy array of shape (y.size, x.size) with the generated noise
              for the supplied coordinates

    >>> rng = numpy.random.default_rng(seed=0)
    >>> ix, iy = rng.random(2), rng.random(2)
    >>> noise2array(ix, iy)
    array([[ 0.00449931, -0.01807883],
           [-0.00203524, -0.02358477]])

**opensimplex.noise3(x, y, z)**

    Generate 3D OpenSimplex noise from X,Y,Z coordinates.
    :param x: x coordinate as float
    :param y: y coordinate as float
    :param z: z coordinate as float
    :return:  generated 3D noise as float, between -1.0 and 1.0

    >>> noise3(0.5, 0.5, 0.5)
    0.39504955501618155

**opensimplex.noise3array(x, y, z)**

    Generates 3D OpenSimplex noise using Numpy arrays for increased performance.
    :param x: numpy array of x-coords
    :param y: numpy array of y-coords
    :param z: numpy array of z-coords
    :return:  3D numpy array of shape (z.size, y.size, x.size) with the generated
              noise for the supplied coordinates

    >>> rng = numpy.random.default_rng(seed=0)
    >>> ix, iy, iz = rng.random(2), rng.random(2), rng.random(2)
    >>> noise3array(ix, iy, iz)
    array([[[0.54942818, 0.54382411],
            [0.54285204, 0.53698967]],
           [[0.48107672, 0.4881196 ],
            [0.45971748, 0.46684901]]])

**opensimplex.noise4(x, y, z, w)**

    Generate 4D OpenSimplex noise from X,Y,Z,W coordinates.
    :param x: x coordinate as float
    :param y: y coordinate as float
    :param z: z coordinate as float
    :param w: w coordinate as float
    :return:  generated 4D noise as float, between -1.0 and 1.0

    >>> noise4(0.5, 0.5, 0.5, 0.5)
    0.04520359600370195

**opensimplex.noise4array(x, y, z, w)**

    Generates 4D OpenSimplex noise using Numpy arrays for increased performance.
    :param x: numpy array of x-coords
    :param y: numpy array of y-coords
    :param z: numpy array of z-coords
    :param w: numpy array of w-coords
    :return:  4D numpy array of shape (w.size, z.size, y.size, x.size) with the
              generated noise for the supplied coordinates

    >>> rng = numpy.random.default_rng(seed=0)
    >>> ix, iy, iz, iw = rng.random(2), rng.random(2), rng.random(2), rng.random(2)
    >>> noise4array(ix, iy, iz, iw)
    array([[[[0.30334626, 0.29860705],
             [0.28271858, 0.27805178]],
            [[0.26601215, 0.25305428],
             [0.23387872, 0.22151356]]],
           [[[0.3392759 , 0.33585534],
             [0.3343468 , 0.33118285]],
            [[0.36930335, 0.36046537],
             [0.36360679, 0.35500328]]]])

## FAQ

- What does the distribution of the noise values look like?

![Noise Distribution](images/distribution.png)

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

    > If you read the [patent
    > claims](http://www.google.com/patents/US6867776):
    >
    > 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].

[Reddit]: https://www.reddit.com/r/proceduralgeneration/comments/2gu3e7/like_perlins_simplex_noise_but_dont_like_the/ckmqz2y


## Credits

- Kurt Spencer - Original work
- Owen Raccuglia - Test cases, [Go Module]
- /u/redblobgames - Fixed conversion for Java's long type, see [Reddit]

And all the other [Contributors] and [Bug Hunters]. Thanks!

[Go Module]: https://github.com/ojrac/opensimplex-go
[Reddit]: https://old.reddit.com/r/proceduralgeneration/comments/327zkm/repeated_patterns_in_opensimplex_python_port/cq8tth7/
[Contributors]: https://code.larus.se/lmas/opensimplex/activity/contributors
[Bug Hunters]: https://code.larus.se/lmas/opensimplex/issues?state=closed

## 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.

## Example Output

More example code and trinkets can be found in the [examples] directory.

[examples]: https://code.larus.se/lmas/opensimplex/src/branch/master/examples

Example images visualising 2D, 3D and 4D noise on a 2D plane, using the default seed:

<img alt="Abstract black and white blobs visualizing 2D opensimplex noise on a 2D plane" src="images/noise2d.png">
<img alt="Abstract black and white blobs visualizing 3D opensimplex noise on a 2D plane" src="images/noise3d.png">
<img alt="Abstract black and white blobs visualizing 4D opensimplex noise on a 2D plane" src="images/noise4d.png">