.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fractals_chaos/dla/plot_01_dla_cluster.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_dla_plot_01_dla_cluster.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_fractals_chaos_dla_plot_01_dla_cluster.py:


Diffusion-limited aggregation
===================================

Grows a cluster by releasing random walkers that stick on first contact,
and measures its fractal dimension from the mass-radius relation
N(r) ~ r^D.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.fractals_chaos import dla_cluster








.. GENERATED FROM PYTHON SOURCE LINES 17-19

Grow and draw the cluster
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-27

.. code-block:: Python


    cluster = dla_cluster(12000, seed=0)
    fig, ax = plt.subplots(figsize=(6, 6))
    ax.scatter(*cluster.T, c=np.arange(len(cluster)), cmap="viridis", s=0.5)
    ax.set_aspect("equal")
    ax.axis("off")
    ax.set_title(f"{len(cluster)} particles, colored by arrival time")




.. image-sg:: /api/gallery/fractals_chaos/dla/images/sphx_glr_plot_01_dla_cluster_001.png
   :alt: 9323 particles, colored by arrival time
   :srcset: /api/gallery/fractals_chaos/dla/images/sphx_glr_plot_01_dla_cluster_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, '9323 particles, colored by arrival time')



.. GENERATED FROM PYTHON SOURCE LINES 28-30

Mass-radius scaling
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 30-44

.. code-block:: Python


    r = np.sqrt((cluster**2).sum(axis=1))
    radii = np.logspace(np.log10(5), np.log10(r.max() / 2), 12)
    mass = np.array([(r < rho).sum() for rho in radii])
    slope = np.polyfit(np.log(radii), np.log(mass), 1)[0]
    print(f"mass-radius dimension D = {slope:.3f} (Witten and Sander: about 1.7)")

    fig, ax = plt.subplots()
    ax.loglog(radii, mass, "o", label="particles within radius r")
    ax.loglog(radii, mass[0] * (radii / radii[0]) ** slope, "--", label=f"slope {slope:.2f}")
    ax.loglog(radii, mass[0] * (radii / radii[0]) ** 2, ":", label="slope 2 (compact disk)")
    ax.set_xlabel("r")
    ax.set_ylabel("N(r)")
    ax.legend()



.. image-sg:: /api/gallery/fractals_chaos/dla/images/sphx_glr_plot_01_dla_cluster_002.png
   :alt: plot 01 dla cluster
   :srcset: /api/gallery/fractals_chaos/dla/images/sphx_glr_plot_01_dla_cluster_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    mass-radius dimension D = 1.663 (Witten and Sander: about 1.7)

    <matplotlib.legend.Legend object at 0x1196e27b0>




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

   **Total running time of the script:** (0 minutes 0.771 seconds)


.. _sphx_glr_download_api_gallery_fractals_chaos_dla_plot_01_dla_cluster.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_dla_cluster.ipynb <plot_01_dla_cluster.ipynb>`

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

      :download:`Download Python source code: plot_01_dla_cluster.py <plot_01_dla_cluster.py>`

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

      :download:`Download zipped: plot_01_dla_cluster.zip <plot_01_dla_cluster.zip>`


.. only:: html

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

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