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

.. only:: html

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

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

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

.. _sphx_glr__gallery_misc_lorenz_animation.py:


Lorenz System Animation
=======================

Example of the Lorenz attractor.

.. GENERATED FROM PYTHON SOURCE LINES 7-93



.. image-sg:: /_gallery/misc/images/sphx_glr_lorenz_animation_001.webp
   :alt: lorenz animation
   :srcset: /_gallery/misc/images/sphx_glr_lorenz_animation_001.webp
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/pygfx/objects/_ruler.py:266: RuntimeWarning: divide by zero encountered in divide
      screen_full = (ndc_full[:, :2] / ndc_full[:, 3:4]) * half_canvas_size
    /opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/pygfx/objects/_ruler.py:266: RuntimeWarning: invalid value encountered in divide
      screen_full = (ndc_full[:, :2] / ndc_full[:, 3:4]) * half_canvas_size
    /opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/site-packages/pygfx/objects/_ruler.py:278: RuntimeWarning: invalid value encountered in divide
      screen_sel = (ndc_sel[:, :2] / ndc_sel[:, 3:4]) * half_canvas_size
    /home/runner/work/fastplotlib/fastplotlib/fastplotlib/graphics/_features/_base.py:18: UserWarning: casting float64 array to float32
      warn(f"casting {array.dtype} array to float32")







|

.. code-block:: Python


    # test_example = false

    import fastplotlib as fpl
    import numpy as np


    # generate data
    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 = 3_000

    lorenz_data = np.empty((5, num_steps + 1, 3))

    for i in range(5):
        xyzs = np.empty((num_steps + 1, 3))  # Need one more for the initial values
        xyzs[0] = (0., (i * 0.3) + 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 j in range(num_steps):
            xyzs[j + 1] = xyzs[j] + lorenz(xyzs[j]) * dt

        lorenz_data[i] = xyzs

    figure = fpl.Figure(
        cameras="3d",
        controller_types="fly",
        size=(700, 560)
    )

    lorenz_line = figure[0, 0].add_line_collection(data=lorenz_data, thickness=.1, cmap="tab10")

    scatter_markers = list()

    for graphic in lorenz_line:
        marker = figure[0, 0].add_scatter(graphic.data.value[0], sizes=16, colors=graphic.colors[0])
        scatter_markers.append(marker)

    # initialize time
    time = 0


    def animate(subplot):
        global time

        time += 2

        if time >= xyzs.shape[0]:
            time = 0

        for scatter, g in zip(scatter_markers, lorenz_line):
            scatter.data = g.data.value[time]


    figure[0, 0].add_animations(animate)

    figure.show()

    # set initial camera position to make animation in gallery render better
    figure[0, 0].camera.world.z = 80

    # NOTE: `if __name__ == "__main__"` is NOT how to use fastplotlib interactively
    # please see our docs for using fastplotlib interactively in ipython and jupyter
    if __name__ == "__main__":
        print(__doc__)
        fpl.run()


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

   **Total running time of the script:** (0 minutes 19.342 seconds)


.. _sphx_glr_download__gallery_misc_lorenz_animation.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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