.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/combinatorics/sequences/plot_03_gray_code.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_combinatorics_sequences_plot_03_gray_code.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_combinatorics_sequences_plot_03_gray_code.py:


Gray codes: counting one bit at a time
============================================

Lists the reflected binary Gray code, checks that neighbouring codes
differ in exactly one bit, and compares the number of bit flips needed
to count through all n-bit words with ordinary binary counting.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.combinatorics import gray_code








.. GENERATED FROM PYTHON SOURCE LINES 17-19

The 4-bit reflected Gray code
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-24

.. code-block:: Python


    codes = gray_code(4)
    for k, g in enumerate(codes):
        print(f"{k:2d}: binary {k:04b}  gray {g:04b}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

     0: binary 0000  gray 0000
     1: binary 0001  gray 0001
     2: binary 0010  gray 0011
     3: binary 0011  gray 0010
     4: binary 0100  gray 0110
     5: binary 0101  gray 0111
     6: binary 0110  gray 0101
     7: binary 0111  gray 0100
     8: binary 1000  gray 1100
     9: binary 1001  gray 1101
    10: binary 1010  gray 1111
    11: binary 1011  gray 1110
    12: binary 1100  gray 1010
    13: binary 1101  gray 1011
    14: binary 1110  gray 1001
    15: binary 1111  gray 1000




.. GENERATED FROM PYTHON SOURCE LINES 25-27

As a picture: one column changes per row
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 27-35

.. code-block:: Python


    bits = np.array([[(g >> (3 - b)) & 1 for b in range(4)] for g in codes])
    fig, ax = plt.subplots(figsize=(3, 6))
    ax.imshow(bits, cmap="Greys", aspect="auto")
    ax.set_xlabel("bit")
    ax.set_ylabel("step")
    ax.set_title("4-bit Gray code")




.. image-sg:: /api/gallery/combinatorics/sequences/images/sphx_glr_plot_03_gray_code_001.png
   :alt: 4-bit Gray code
   :srcset: /api/gallery/combinatorics/sequences/images/sphx_glr_plot_03_gray_code_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(0.5, 1.0, '4-bit Gray code')



.. GENERATED FROM PYTHON SOURCE LINES 36-38

Bit flips to count through every word
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 38-44

.. code-block:: Python


    for n in range(2, 9):
        binary_flips = sum(bin(k ^ (k + 1)).count("1") for k in range(2**n - 1))
        gray = gray_code(n)
        gray_flips = sum(bin(a ^ b).count("1") for a, b in zip(gray, gray[1:]))
        print(f"n = {n}: binary counting flips {binary_flips} bits, Gray code flips {gray_flips}")




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    n = 2: binary counting flips 4 bits, Gray code flips 3
    n = 3: binary counting flips 11 bits, Gray code flips 7
    n = 4: binary counting flips 26 bits, Gray code flips 15
    n = 5: binary counting flips 57 bits, Gray code flips 31
    n = 6: binary counting flips 120 bits, Gray code flips 63
    n = 7: binary counting flips 247 bits, Gray code flips 127
    n = 8: binary counting flips 502 bits, Gray code flips 255





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.017 seconds)


.. _sphx_glr_download_api_gallery_combinatorics_sequences_plot_03_gray_code.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_03_gray_code.ipynb <plot_03_gray_code.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_03_gray_code.py <plot_03_gray_code.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_03_gray_code.zip <plot_03_gray_code.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_