Plotting External Rays on the Mandelbrot Set

[bbarros50]

This is the second ticket for my Google Summer of Code project (the first was #23257: Plotting the Mandelbrot set). I have added the external_ray function to the Complex Dynamics folder. This function allows the user to pass in an angle or list of angles and returns the plot of the external rays for the given angles on the Mandelbrot set. For more information on my Google Summer of Code Project you can visit the following link: ​https://benbarros.wordpress.com/

Depends on #23257

CC: @bhutz @sagetrac-atowsley

Component: dynamics

Keywords: GSoC2017, ComplexDynamics

Author: Ben Barros

Branch/Commit: 7a7d890

Reviewer: Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/23425

[bbarros50]

Branch: u/bbarros/23425

[bbarros50]

Commit: 6280217

[bbarros50]

Last 10 new commits:

6a9f953	23257: Fixed documentation and syntax
f74fac8	Merge branch 'master' into 23257
e1a3791	23257: Changed to lazy_import in complex_dynamics/all.py
1afa332	23257: Fixed merge conflict and doctests
9b6738b	23257: Cython, Python 3 improvements, Color widget added
a1d02e4	23257: Changed fast_mandel_plot to fast_mandelbrot_plot
8aae69c	23257: Changed default for interact to False
f52fb3f	23257: Added complex_dynamics to dynamics/index.rst
607cc2d	Merge branch 'develop' of git://trac.sagemath.org/sage into ExternalRays
6280217	23425: Added external_ray function, helper functions.

[bhutz]

comment:3

I haven't had a chance to do much testing yet. So far it appears to work well in the notebook, but I need to do a thorough code review. Here is at least one error:

sage: external_ray(3/7,D=70)
ValueError: cannot convert float NaN to integer

if you zoom in, it looks like something is going wrong with the later Newton's methods

sage: external_ray(3/7,D=60, image_width=0.1, x_center=-1.75)

here are a few minor things I picked out:

• need to input check 0<= ray <=1

• need to wrap the long lines (90 characters is the typical limit)

• add a ray color example

• change the first long example to a decimal

• in warning:

  • typo 'specify the which'

• you shouldn't need to keywords for the mandelbrot set here.

It would be cleaner to default image to None. Then after you .pop image you check if 'is None' and if true mandelbrot_plot. If you use .get() instead of .pop() you can pass kwds directly to mandelbrot_plot.

• you can just say, theta = list(theta) instead of

    if type(theta) != list:
        theta = [theta]

• put something in the doc about: if the ray doesn't reach the boundary increase D, if the ray looks jagged increase S. Has a speed penalty

[bhutz]

Reviewer: Ben Hutz

[sagetrac-git]

Changed commit from 6280217 to 9aabbed

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

9aabbed

23425: Bug fixes, edited examples

[bbarros50]

comment:6

The following code didn't work:

theta = list(theta)

Since it returns the following error:

TypeError: 'sage.rings.integer.Integer' object is not iterable

[bhutz]

comment:7

Just one very minor comment

In the description of the input R there is an extra word or something. Also, I'd add the comment similar to the other parameters that if R is too small Newton's method may not converge to the correct ray.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

7a7d890

23425: Updated documentation

[sagetrac-git]

Changed commit from 9aabbed to 7a7d890

[vbraun]

Changed branch from u/bbarros/23425 to 7a7d890