nengolib.stats.leech_kissing

nengolib.stats.leech_kissing(cache_file=None)[source]

Generates the 196,560 “kissing points” in 24 dimensions.

These are the points that are unit distance from the origin in the 24–dimensional Leech lattice. [1] Such points give the optimal configuration for sphere-packing in 24 dimensions. [2]

Parameters:

cache_file : string, optional

Name of file to cache/retrieve the results of this function call. Defaults to Nengo’s cache directory + "leech_kissing.npy".

Returns:

(196560, 24) np.array

The kissing points in 24 dimensions.

References

[1]https://en.wikipedia.org/wiki/Leech_lattice
[2]https://en.wikipedia.org/wiki/Kissing_number_problem

Examples

>>> from nengolib.stats import leech_kissing
>>> pts = leech_kissing()

We can visualize some of the lattice structure by projections into two dimensions. This scatter plot will look the same regardless of which two coordinates are chosen.

>>> import matplotlib.pyplot as plt
>>> plt.scatter(pts[:, 0], pts[:, 1], s=50)
>>> plt.show()

(Source code)

_images/nengolib-stats-leech_kissing-1.png