.. _sphx_glr_api_gallery_fractals_chaos_box_counting:

Box-counting dimension
-----------------------

Estimating fractal dimension from a point cloud via box-counting.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Generates the Sierpinski triangle via the chaos game and estimates its box-counting dimension, comparing against the known closed-form value \log 3/\log 2 \approx 1.585.">

.. only:: html

  .. image:: /api/gallery/fractals_chaos/box_counting/images/thumb/sphx_glr_plot_01_sierpinski_dimension_thumb.png
    :alt:

  :doc:`/api/gallery/fractals_chaos/box_counting/plot_01_sierpinski_dimension`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Box-counting dimension of the Sierpinski triangle</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Starts from [0, 1] and repeatedly removes the open middle third of every remaining interval. After n steps there are 2^n intervals of total length (2/3)^n \to 0, yet the limit set is uncountable. Box counting recovers its fractional dimension \log 2/\log 3 \approx 0.631.">

.. only:: html

  .. image:: /api/gallery/fractals_chaos/box_counting/images/thumb/sphx_glr_plot_02_cantor_set_dimension_thumb.png
    :alt:

  :doc:`/api/gallery/fractals_chaos/box_counting/plot_02_cantor_set_dimension`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cantor's middle-thirds set and its dimension</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/fractals_chaos/box_counting/plot_01_sierpinski_dimension
   /api/gallery/fractals_chaos/box_counting/plot_02_cantor_set_dimension