.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fractals_chaos/box_counting/plot_01_sierpinski_dimension.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_fractals_chaos_box_counting_plot_01_sierpinski_dimension.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_fractals_chaos_box_counting_plot_01_sierpinski_dimension.py:


Box-counting dimension of the Sierpinski triangle
=======================================================

Generates the Sierpinski triangle via the chaos game and estimates its
box-counting dimension, comparing against the known closed-form value
:math:`\log 3/\log 2 \approx 1.585`.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

    import numpy as np

    from mathematicskit.fractals_chaos import SierpinskiTriangle, box_counting_dimension
    from mathematicskit.fractals_chaos.visualizers.plots import plot_box_counting, plot_ifs_points








.. GENERATED FROM PYTHON SOURCE LINES 17-19

Generate the point cloud and estimate its dimension
-----------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-25

.. code-block:: Python


    points = SierpinskiTriangle().generate(60000, seed=0)
    result = box_counting_dimension(points)
    print(f"estimated dimension: {result.dimension:.4f}")
    print(f"exact value log(3)/log(2): {np.log(3.0) / np.log(2.0):.4f}")





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

 .. code-block:: none

    estimated dimension: 1.5520
    exact value log(3)/log(2): 1.5850




.. GENERATED FROM PYTHON SOURCE LINES 26-28

Visualize the point cloud and the log-log fit
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 28-31

.. code-block:: Python


    plot_ifs_points(points)
    plot_box_counting(result)



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /api/gallery/fractals_chaos/box_counting/images/sphx_glr_plot_01_sierpinski_dimension_001.png
         :alt: plot 01 sierpinski dimension
         :srcset: /api/gallery/fractals_chaos/box_counting/images/sphx_glr_plot_01_sierpinski_dimension_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /api/gallery/fractals_chaos/box_counting/images/sphx_glr_plot_01_sierpinski_dimension_002.png
         :alt: Box-counting dimension
         :srcset: /api/gallery/fractals_chaos/box_counting/images/sphx_glr_plot_01_sierpinski_dimension_002.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <Axes: title={'center': 'Box-counting dimension'}, xlabel='1 / box size', ylabel='box count'>




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

   **Total running time of the script:** (0 minutes 0.313 seconds)


.. _sphx_glr_download_api_gallery_fractals_chaos_box_counting_plot_01_sierpinski_dimension.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_sierpinski_dimension.ipynb <plot_01_sierpinski_dimension.ipynb>`

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

      :download:`Download Python source code: plot_01_sierpinski_dimension.py <plot_01_sierpinski_dimension.py>`

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

      :download:`Download zipped: plot_01_sierpinski_dimension.zip <plot_01_sierpinski_dimension.zip>`


.. only:: html

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

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