.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fractals_chaos/lsystems/plot_01_lindenmayer_plants.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_lsystems_plot_01_lindenmayer_plants.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_fractals_chaos_lsystems_plot_01_lindenmayer_plants.py:


Lindenmayer systems: from algae to plants
===============================================

Runs Lindenmayer's 1968 algae system, whose string lengths are Fibonacci
numbers, and draws a Koch curve and a branching plant with turtle
graphics.

.. GENERATED FROM PYTHON SOURCE LINES 11-15

.. code-block:: Python

    import matplotlib.pyplot as plt

    from mathematicskit.fractals_chaos import lsystem, turtle_path








.. GENERATED FROM PYTHON SOURCE LINES 16-18

Lindenmayer's algae
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 18-23

.. code-block:: Python


    for n in range(7):
        word = lsystem("A", {"A": "AB", "B": "A"}, n)
        print(f"n = {n}: {word} (length {len(word)})")





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

 .. code-block:: none

    n = 0: A (length 1)
    n = 1: AB (length 2)
    n = 2: ABA (length 3)
    n = 3: ABAAB (length 5)
    n = 4: ABAABABA (length 8)
    n = 5: ABAABABAABAAB (length 13)
    n = 6: ABAABABAABAABABAABABA (length 21)




.. GENERATED FROM PYTHON SOURCE LINES 24-26

A Koch curve and a fractal plant
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 26-37

.. code-block:: Python


    koch = turtle_path(lsystem("F", {"F": "F+F--F+F"}, 4), 60, heading=0)
    plant = turtle_path(lsystem("X", {"X": "F+[[X]-X]-F[-FX]+X", "F": "FF"}, 5), 25, heading=65)

    fig, axes = plt.subplots(1, 2, figsize=(10, 5))
    for ax, lines, title in zip(axes, (koch, plant), ("Koch curve: F -> F+F--F+F", "plant: X -> F+[[X]-X]-F[-FX]+X")):
        for line in lines:
            ax.plot(*line.T, color="darkgreen" if ax is axes[1] else "tab:blue", lw=0.6)
        ax.set_aspect("equal")
        ax.axis("off")
        ax.set_title(title, fontsize=10)



.. image-sg:: /api/gallery/fractals_chaos/lsystems/images/sphx_glr_plot_01_lindenmayer_plants_001.png
   :alt: Koch curve: F -> F+F--F+F, plant: X -> F+[[X]-X]-F[-FX]+X
   :srcset: /api/gallery/fractals_chaos/lsystems/images/sphx_glr_plot_01_lindenmayer_plants_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.070 seconds)


.. _sphx_glr_download_api_gallery_fractals_chaos_lsystems_plot_01_lindenmayer_plants.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_lindenmayer_plants.ipynb <plot_01_lindenmayer_plants.ipynb>`

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

      :download:`Download Python source code: plot_01_lindenmayer_plants.py <plot_01_lindenmayer_plants.py>`

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

      :download:`Download zipped: plot_01_lindenmayer_plants.zip <plot_01_lindenmayer_plants.zip>`


.. only:: html

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

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