.. _sphx_glr_api_gallery_fractals_chaos_mandelbrot_julia:

Mandelbrot and Julia sets
---------------------------

Escape-time generation of the Mandelbrot set and Julia sets.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Iterates the quadratic map z \mapsto z^2 + c from every starting point z_0 of a grid. Points whose orbits stay bounded form the filled Julia set; its boundary, the Julia set, separates the Fatou set, where nearby orbits behave alike, from the region where orbits escape to infinity. Changing c turns the Julia set from a circle into a fractal curve or a disconnected dust.">

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  .. image:: /api/gallery/fractals_chaos/mandelbrot_julia/images/thumb/sphx_glr_plot_01_julia_sets_thumb.png
    :alt:

  :doc:`/api/gallery/fractals_chaos/mandelbrot_julia/plot_01_julia_sets`

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      <div class="sphx-glr-thumbnail-title">Fatou and Julia: Julia sets of z -> z^2 + c</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Colours every parameter c by how quickly the orbit of z_0 = 0 under z \mapsto z^2 + c escapes. The black region, the Mandelbrot set, is the set of c whose orbit stays bounded -- equivalently, whose Julia set is connected. Zooming into its boundary reveals ever finer detail, including small copies of the whole set.">

.. only:: html

  .. image:: /api/gallery/fractals_chaos/mandelbrot_julia/images/thumb/sphx_glr_plot_02_mandelbrot_set_thumb.png
    :alt:

  :doc:`/api/gallery/fractals_chaos/mandelbrot_julia/plot_02_mandelbrot_set`

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      <div class="sphx-glr-thumbnail-title">The Mandelbrot set</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/fractals_chaos/mandelbrot_julia/plot_01_julia_sets
   /api/gallery/fractals_chaos/mandelbrot_julia/plot_02_mandelbrot_set