Showcase example: (kind of mandatory) Mandelbrot set #7447

rougier · 2016-11-12T10:53:22Z

This is a rendering of the Mandelbrot set. I think it is reasonably good looking (using normalized recount, adapted normalized colormap and shading).

stonebig · 2016-11-12T17:56:32Z

I get these error message testing under python-3.6.0b3, don't know if it's important:

C:/WinPython/basedir36/build/winpython-64bit-3.6.x.0/notebooks/mandelbrot.py:41: RuntimeWarning: invalid value encountered in log
M = np.nan_to_num(N + 1 - np.log(np.log(abs(Z)))/np.log(2) + log_horizon)
C:\WinPython\basedir36\build\winpython-64bit-3.6.x.0\python-3.6.0b3.amd64\lib\site-packages\matplotlib\font_manager.py:1288: UserWarning: findfont: Font family ['Source Sans Pro Light'] not found. Falling back to Bitstream Vera Sans
(prop.get_family(), self.defaultFamily[fontext]))

image seems generated ok anyway

.... oups! you warned of the error in comment.. sorry for the noise

rougier · 2016-11-12T18:03:20Z

@stonebig I removed the second warning (font specification).

anntzer · 2016-11-12T21:18:51Z

examples/showcase/mandelbrot.py

+    # Some advertisement for matplotlib
+    ax.text(xmin+0.025, ymin+0.025,
+            "The Mandelbrot fractal set\n"
+            "Rendered with matplotlib 2.0, 2016 — http://www.matplotlib.org",


Dynamically fetch the version and the year here, perhaps?

Yes, good point.

NelleV · 2016-11-12T23:24:10Z

Hi Nicolas,

Can you also please add a docstring with a title and a description of the example? It should be formatted as follow:

"""
===============================
Colormaps alter your perception
===============================

Here I plot the function

.. math:: f(x, y) = \sin(x) + \cos(y)

with different colormaps. Look at how colormaps alter your perception!
"""

rougier · 2016-11-13T05:39:46Z

Hi Nelle,

Sure.

QuLogic · 2016-11-13T06:05:00Z

examples/showcase/mandelbrot.py

+    return Z, N
+
+
+if __name__ == '__main__':


I don't think this conditional block is necessary.

It doesn't hurt and allow to import mandelbrot if you want to experience with it.

QuLogic · 2016-11-13T06:05:06Z

examples/showcase/mandelbrot.py

+    Z, N = mandelbrot_set(xmin, xmax, ymin, ymax, xn, yn, maxiter, horizon)
+
+    # Normalized recount as explained in:
+    # http://linas.org/art-gallery/escape/smooth.html


QuLogic · 2016-11-13T06:06:22Z

examples/showcase/mandelbrot.py

+
+    # This line will generate warnings for null values but it is faster to
+    # process them afterwards using the nan_to_num
+    M = np.nan_to_num(N + 1 - np.log(np.log(abs(Z)))/np.log(2) + log_horizon)


with np.errstate(invalid='ignore'): M = np.nan_to_num(...)

?

QuLogic · 2016-11-13T06:07:27Z

examples/showcase/mandelbrot.py

+    # process them afterwards using the nan_to_num
+    M = np.nan_to_num(N + 1 - np.log(np.log(abs(Z)))/np.log(2) + log_horizon)
+
+    dpi = 72


Is changing dpi important?

More or less. I wanted to be sure of the approximate pixel resolution.

I'm not sure I understand. The dataset is 3000 samples wide (xn) and the figure is 10 inches wide (width), giving an effective resolution of 300 dpi (if corresponding 1-to-1.) With dpi=72, the data needs to be resampled at a ratio of 25:6 = ~4.166667, which seems odd.

Oops, just realized I missed the /2, so it's really 1500 samples wide with effective resolution of 150 dpi, and resampling ratio of 25:12 = ~2.083333. But in that case, how about making it exactly 2 by setting dpi=75?

QuLogic · 2016-11-13T06:09:46Z

examples/showcase/mandelbrot.py

+
+    # Shaded rendering
+    light = colors.LightSource(azdeg=315, altdeg=10)
+    M = light.shade(M, cmap=plt.cm.hot, vert_exag=1.5,


Should we use our fancy new colour maps (magma, inferno, or plasma)? I'm not sure how well they work with shading though.

I tried but output was not as nice as with the hot colormap.

QuLogic · 2016-11-13T06:11:30Z

examples/showcase/mandelbrot.py

+
+    # Some advertisement for matplotlib
+    year = time.strftime("%Y")
+    major, minor, micro = matplotlib.__version__.split('.')


You never know what might be in the local version identifier, so you should add maxsplit=3 here.

Didn't know about this one, thanks.

QuLogic · 2016-11-13T06:11:49Z

examples/showcase/mandelbrot.py

+            % (major, minor, year))
+    ax.text(xmin+.025, ymin+.025, text, color="white", fontsize=12, alpha=0.5)
+
+    # plt.savefig("mandelbrot.png")


QuLogic · 2016-11-15T01:24:03Z

examples/showcase/mandelbrot.py

+
+    # Some advertisement for matplotlib
+    year = time.strftime("%Y")
+    major, minor, micro = matplotlib.__version__.split('.', maxsplit=3)


Sorry, got the number wrong; should be 2.

NelleV · 2016-11-15T17:46:47Z

Thanks @rougier ! This looks goot to me!

DOC: Showcase example: (kind of mandatory) Mandelbrot set

tacaswell · 2016-11-16T02:54:24Z

backported to v2.x as 1209e70

Thanks @rougier

jniediek · 2016-11-17T10:08:49Z

I think there are several bugs in this example, which make it impossible to run it with python2.7, which breaks the documentation build process.

As I'm unfamiliar with matplotlib's policy for examples, I'll just list here what I consider to be bugs (and fixes):

python2.7 mandelbrot.py
File "mandelbrot.py", line 71
SyntaxError: Non-ASCII character '\xe2' in file mandelbrot.py on line 71, but no encoding declared;     see http://python.org/dev/peps/pep-0263/ for details

Adding # -*- coding: utf-8 -*- as first line:

python2.7 mandelbrot.py 
Traceback (most recent call last):
File "mandelbrot.py", line 70, in <module>
major, minor, micro = matplotlib.__version__.split('.', maxsplit=2)
TypeError: split() takes no keyword arguments

Changing to

major, minor, micro = matplotlib.__version__.split('.')[:3]

And changing the next line to

text = ("The Mandelbrot fractal set\n"
        "Rendered with matplotlib %s.%s, %s — http://matplotlib.org".decode('utf-8')
        % (major, minor, year))

It finally works with python2.7.

I have a feeling that using six and from __future__ import would be appropriate here, but as I said, I'm unfamiliar with the policies.

tacaswell · 2016-11-17T13:13:13Z

@jniediek already fixed: #7473

I strongly encourage you to move to python3 as soon as possible.

See https://python-3-for-scientists.readthedocs.io/en/latest/ and https://python3statement.github.io/

TLDR: You get nice stuff for switching and you are going start losing access to new versions of libraries in 2018-2020 time frame.

Added the (kind of mandatory) Mandelbrot set

2af3aae

Removed font family specification

7fe3739

tacaswell added this to the 2.0.1 (next bug fix release) milestone Nov 12, 2016

tacaswell added the Documentation label Nov 12, 2016

anntzer reviewed Nov 12, 2016

View reviewed changes

Dynamic version and year in displayed text + code simplification

7c0d92a

Added docstring

9542a8e

Added info about computation time

68247ea

QuLogic reviewed Nov 13, 2016

View reviewed changes

rougier added 2 commits November 13, 2016 07:55

Small modifications

fc5668f

Small typo

30c894d

QuLogic reviewed Nov 15, 2016

View reviewed changes

Fix maxsplit=2

78fc1fa

NelleV changed the title ~~Showcase example: (kind of mandatory) Mandelbrot set~~ [MRG+1] Showcase example: (kind of mandatory) Mandelbrot set Nov 15, 2016

NelleV approved these changes Nov 15, 2016

View reviewed changes

tacaswell merged commit 631e079 into matplotlib:master Nov 16, 2016

tacaswell added a commit that referenced this pull request Nov 16, 2016

Merge pull request #7447 from rougier/mandelbrot

1209e70

DOC: Showcase example: (kind of mandatory) Mandelbrot set

QuLogic changed the title ~~[MRG+1] Showcase example: (kind of mandatory) Mandelbrot set~~ Showcase example: (kind of mandatory) Mandelbrot set Nov 16, 2016

QuLogic modified the milestones: 2.0.1 (next bug fix release), 2.0 (style change major release) Dec 7, 2016

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Showcase example: (kind of mandatory) Mandelbrot set #7447

Showcase example: (kind of mandatory) Mandelbrot set #7447

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NelleV commented Nov 12, 2016

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NelleV commented Nov 15, 2016

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tacaswell commented Nov 16, 2016

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jniediek commented Nov 17, 2016

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tacaswell commented Nov 17, 2016

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rougier commented Nov 12, 2016 •

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stonebig commented Nov 12, 2016 •

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