.. _sphx_glr_api_gallery_chaos_interactive_and_animation:

Interactive and Animated Visualizers
------------------------------------

Examples illustrating the dynamic visualizers in
:mod:`physicskit.chaos.visualizers.dynamic_plots`: a live Matplotlib animation of a
billiard trajectory alongside its growing Poincare section, interactive
Plotly figures (2D and 3D), and trajectory color-coding.

.. note::
   Run directly (``python examples/.../plot_x.py``), the Matplotlib animation
   opens an interactive window and the Plotly figures open in a browser tab.
   In the built documentation, the animation is instead embedded as inline
   HTML5 video (via Sphinx-Gallery's
   `animation scraper <https://sphinx-gallery.github.io/stable/configuration.html#animations>`_,
   enabled by ``matplotlib_animations: True`` in ``docs/source/conf.py``) and
   the Plotly figures as interactive embedded charts (via
   ``plotly.io._sg_scraper.plotly_sg_scraper``, Plotly's own Sphinx-Gallery
   scraper).


.. 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="The billiard animated here is the Bunimovich stadium: two straight edges, y=\pm r for |x|\le a, joined by semicircular caps of radius r centered at (\pm a, 0). A billiard particle moves in a straight line at constant speed and undergoes specular reflection off this boundary,">

.. only:: html

  .. image:: /api/gallery/chaos/interactive_and_animation/images/thumb/sphx_glr_plot_billiard_animation_thumb.gif
    :alt:

  :doc:`/api/gallery/chaos/interactive_and_animation/plot_billiard_animation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Animated Billiard Trajectory</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Coloring a trajectory by a per-point scalar -- rather than drawing it in a single flat color -- can make a plot&#x27;s structure much easier to read: which parts of a billiard came early or late, or where a continuous trajectory is moving fast versus slow. Two systems are colored below: the Bunimovich stadium billiard (two straight edges joined by semicircular caps of radius r, with specular reflection \mathbf{v}&#x27; = \mathbf{v} - 2(\mathbf{v}\cdot\mathbf{n})\,\mathbf{n} at the boundary), and the Lorenz attractor,">

.. only:: html

  .. image:: /api/gallery/chaos/interactive_and_animation/images/thumb/sphx_glr_plot_colored_trajectories_thumb.png
    :alt:

  :doc:`/api/gallery/chaos/interactive_and_animation/plot_colored_trajectories`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Trajectory Color-Coding</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Alongside the Matplotlib helpers, physicskit.chaos.visualizers.dynamic_plots provides interactive Plotly figures: a trajectory you can pan and zoom, and an interactive Poincare section you can hover over to inspect individual bounce points. The billiard used here is the Sinai billiard: a square cell, |x|\le L/2,\ |y|\le L/2, with a circular scatterer of radius r_s removed from its center, x^2+y^2=r_s^2, off of which the particle undergoes specular reflection, \mathbf{v}&#x27; = \mathbf{v} - 2(\mathbf{v}\cdot\mathbf{n}) \,\mathbf{n}, whenever it strikes the boundary.">

.. only:: html

  .. image:: /api/gallery/chaos/interactive_and_animation/images/thumb/sphx_glr_plot_plotly_trajectory_thumb.png
    :alt:

  :doc:`/api/gallery/chaos/interactive_and_animation/plot_plotly_trajectory`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Interactive Plotly Figures</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/chaos/interactive_and_animation/plot_billiard_animation
   /api/gallery/chaos/interactive_and_animation/plot_colored_trajectories
   /api/gallery/chaos/interactive_and_animation/plot_plotly_trajectory