
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/mplot3d/lorenz_attractor.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. meta::
        :keywords: codex

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gallery_mplot3d_lorenz_attractor.py>`
        to download the full example code.

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

.. _sphx_glr_gallery_mplot3d_lorenz_attractor.py:


================
Lorenz attractor
================

This is an example of plotting Edward Lorenz's 1963 `"Deterministic Nonperiodic
Flow"`_ in a 3-dimensional space using mplot3d.

.. _"Deterministic Nonperiodic Flow":
   https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml

.. note::
   Because this is a simple non-linear ODE, it would be more easily done using
   SciPy's ODE solver, but this approach depends only upon NumPy.

.. GENERATED FROM PYTHON SOURCE LINES 16-63

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np


    def lorenz(xyz, *, s=10, r=28, b=2.667):
        """
        Parameters
        ----------
        xyz : array-like, shape (3,)
           Point of interest in three-dimensional space.
        s, r, b : float
           Parameters defining the Lorenz attractor.

        Returns
        -------
        xyz_dot : array, shape (3,)
           Values of the Lorenz attractor's partial derivatives at *xyz*.
        """
        x, y, z = xyz
        x_dot = s*(y - x)
        y_dot = r*x - y - x*z
        z_dot = x*y - b*z
        return np.array([x_dot, y_dot, z_dot])


    dt = 0.01
    num_steps = 10000

    xyzs = np.empty((num_steps + 1, 3))  # Need one more for the initial values
    xyzs[0] = (0., 1., 1.05)  # Set initial values
    # Step through "time", calculating the partial derivatives at the current point
    # and using them to estimate the next point
    for i in range(num_steps):
        xyzs[i + 1] = xyzs[i] + lorenz(xyzs[i]) * dt

    # Plot
    ax = plt.figure().add_subplot(projection='3d')

    ax.plot(*xyzs.T, lw=0.5)
    ax.set_xlabel("X Axis")
    ax.set_ylabel("Y Axis")
    ax.set_zlabel("Z Axis")
    ax.set_title("Lorenz Attractor")

    plt.show()


.. GENERATED FROM PYTHON SOURCE LINES 64-67

.. tags::
   plot-type: 3D,
   level: intermediate


.. _sphx_glr_download_gallery_mplot3d_lorenz_attractor.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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