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removed math directive from README.rst
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galtay committed Nov 30, 2019
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32 changes: 16 additions & 16 deletions README.rst
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Expand Up @@ -3,17 +3,17 @@ Introduction
============

This is a package to convert between one dimensional distance along a
`Hilbert curve`_, :math:`h`, and :math:`N`-dimensional coordinates,
:math:`(x_0, x_1, ... x_N-1)`. There are two important parameters,
`Hilbert curve`_, ``h``, and ``N``-dimensional coordinates,
``(x_0, x_1, ... x_N-1)``. There are two important parameters,

* :math:`N` -- the number of dimensions (must be > 0)
* :math:`p` -- the number of iterations used in constructing the Hilbert curve (must be > 0)
* ``N`` -- the number of dimensions (must be > 0)
* ``p`` -- the number of iterations used in constructing the Hilbert curve (must be > 0)

We consider an :math:`N`-dimensional `hypercube`_ of side length :math:`2^p`.
This hypercube contains :math:`2^{N p}` unit hypercubes (:math:`2^p` along
We consider an ``N``-dimensional `hypercube`_ of side length ``2^p``.
This hypercube contains ``2^{N p}`` unit hypercubes (``2^p`` along
each dimension). The number of unit hypercubes determine the possible
discrete distances along the Hilbert curve (indexed from 0 to
:math:`2^{N p} - 1`).
``2^{N p} - 1``).


==========
Expand Down Expand Up @@ -77,7 +77,7 @@ The calculations above represent the 512th iteration of the Hilbert curve in 10
The maximum value along any coordinate axis is an integer with 155 digits and the maximum
distance along the curve is an integer with 1542 digits. For comparison,
`an estimate of the number of atoms in the observable universe`_
is :math:`10^{82}` (i.e. an integer with 83 digits).
is ``10^{82}`` (i.e. an integer with 83 digits).

=======
Visuals
Expand All @@ -87,14 +87,14 @@ Visuals
.. figure:: n2_p3.png

The figure above shows the first three iterations of the Hilbert
curve in two (:math:`N=2`) dimensions. The :math:`p=1` iteration is shown
in red, :math:`p=2` in blue, and :math:`p=3` in black.
For the :math:`p=3` iteration, distances, :math:`h`, along the curve are
labeled from 0 to 63 (i.e. from 0 to :math:`2^{N p}-1`). This package
provides methods to translate between :math:`N`-dimensional coordinates and one
dimensional distance. For example, between (:math:`x_0=4, x_1=6`) and
:math:`h=36`. Note that the :math:`p=1` and :math:`p=2` iterations have been
scaled and translated to the coordinate system of the :math:`p=3` iteration.
curve in two (``N=2``) dimensions. The ``p=1`` iteration is shown
in red, ``p=2`` in blue, and ``p=3`` in black.
For the ``p=3`` iteration, distances, ``h``, along the curve are
labeled from 0 to 63 (i.e. from 0 to ``2^{N p}-1``). This package
provides methods to translate between ``N``-dimensional coordinates and one
dimensional distance. For example, between (``x_0=4, x_1=6``) and
``h=36``. Note that the ``p=1`` and ``p=2`` iterations have been
scaled and translated to the coordinate system of the ``p=3`` iteration.


An animation of the same case in 3-D is available on YouTube. To watch the video,
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2 changes: 1 addition & 1 deletion hilbertcurve/__init__.py
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@@ -1,4 +1,4 @@
"""Metadata for this package."""

__package_name__ = "hilbertcurve"
__version__ = "1.0.1"
__version__ = "1.0.3"

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