.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fractals_chaos/curves/plot_05_similarity_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_curves_plot_05_similarity_dimension.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_fractals_chaos_curves_plot_05_similarity_dimension.py:


Hausdorff and Moran: the similarity dimension
===================================================

Solves Moran's equation sum r_i^D = 1 for several self-similar sets and
compares the answers with box-counting estimates computed from the
sets themselves.

.. GENERATED FROM PYTHON SOURCE LINES 11-21

.. code-block:: Python

    import numpy as np

    from mathematicskit.fractals_chaos import (
        SierpinskiCarpet,
        SierpinskiTriangle,
        box_counting_dimension,
        koch_curve,
        similarity_dimension,
    )








.. GENERATED FROM PYTHON SOURCE LINES 22-24

Moran's equation against box counting
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-41

.. code-block:: Python


    cantor_points = np.array([[sum(int(d) * 2 * 3.0 ** -(k + 1) for k, d in enumerate(f"{i:012b}")), 0.0] for i in range(4096)])
    cases = {
        "Cantor set": ([1 / 3] * 2, cantor_points),
        "Koch curve": ([1 / 3] * 4, koch_curve(7)),
        "Sierpinski triangle": ([1 / 2] * 3, SierpinskiTriangle().generate(200000)),
        "Sierpinski carpet": ([1 / 3] * 8, SierpinskiCarpet().generate(300000)),
    }
    for name, (ratios, points) in cases.items():
        if name == "Cantor set":
            points = np.column_stack([points[:, 0], np.zeros(len(points))])
            sizes = np.logspace(-1, -3.3, 10)
            estimate = np.polyfit(np.log(1 / sizes), np.log([len(np.unique(np.floor(points[:, 0] / s))) for s in sizes]), 1)[0]
        else:
            estimate = box_counting_dimension(points).dimension
        print(f"{name:20s} similarity dimension {similarity_dimension(ratios):.4f}, box counting {estimate:.4f}")





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

 .. code-block:: none

    Cantor set           similarity dimension 0.6309, box counting 0.6353
    Koch curve           similarity dimension 1.2619, box counting 1.2771
    Sierpinski triangle  similarity dimension 1.5850, box counting 1.5538
    Sierpinski carpet    similarity dimension 1.8928, box counting 1.8194




.. GENERATED FROM PYTHON SOURCE LINES 42-44

Unequal ratios
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 44-47

.. code-block:: Python


    print(f"\nratios (1/2, 1/4, 1/4): D = {similarity_dimension([0.5, 0.25, 0.25]):.4f}")
    print(f"ratios (0.6, 0.3):      D = {similarity_dimension([0.6, 0.3]):.4f}")




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

 .. code-block:: none


    ratios (1/2, 1/4, 1/4): D = 1.0000
    ratios (0.6, 0.3):      D = 0.8594





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

   **Total running time of the script:** (0 minutes 2.537 seconds)


.. _sphx_glr_download_api_gallery_fractals_chaos_curves_plot_05_similarity_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_05_similarity_dimension.ipynb <plot_05_similarity_dimension.ipynb>`

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

      :download:`Download Python source code: plot_05_similarity_dimension.py <plot_05_similarity_dimension.py>`

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

      :download:`Download zipped: plot_05_similarity_dimension.zip <plot_05_similarity_dimension.zip>`


.. only:: html

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

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