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

    Click :ref:`here <sphx_glr_download_intro_numpy_auto_examples_plot_mandelbrot.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_intro_numpy_auto_examples_plot_mandelbrot.py:


Mandelbrot set
==============

Compute the Mandelbrot fractal and plot it





.. image:: /intro/numpy/auto_examples/images/sphx_glr_plot_mandelbrot_001.png
    :class: sphx-glr-single-img





.. code-block:: python

    import numpy as np
    import matplotlib.pyplot as plt
    from numpy import newaxis

    def compute_mandelbrot(N_max, some_threshold, nx, ny):
        # A grid of c-values
        x = np.linspace(-2, 1, nx)
        y = np.linspace(-1.5, 1.5, ny)

        c = x[:,newaxis] + 1j*y[newaxis,:]

        # Mandelbrot iteration

        z = c

        # The code below overflows in many regions of the x-y grid, suppress
        # warnings temporarily
        with np.warnings.catch_warnings():
            np.warnings.simplefilter("ignore")
            for j in range(N_max):
                z = z**2 + c
            mandelbrot_set = (abs(z) < some_threshold)

        return mandelbrot_set

    mandelbrot_set = compute_mandelbrot(50, 50., 601, 401)

    plt.imshow(mandelbrot_set.T, extent=[-2, 1, -1.5, 1.5])
    plt.gray()
    plt.show()

**Total running time of the script:** ( 0 minutes  0.106 seconds)


.. _sphx_glr_download_intro_numpy_auto_examples_plot_mandelbrot.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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