#11837: Make Newton basin plotting fun and easy
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Reporter: kcrisman | Owner: jason, was
Type: enhancement | Status: new
Priority: major | Milestone:
Component: graphics | Keywords: fractal newton complex plot
Work_issues: | Upstream: N/A
Reviewer: | Author: Karl-Dieter Crisman, SImon King
Merged: | Dependencies:
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Comment(by kcrisman):
Okay, now I have something very naive with iterations. Picture (same
code) [attachment:WithIterations.png here] and code
[attachment:newton_basins_with_iterations.spyx here].
Caveats:
* I am pretty sure that the lightness thing could be improved - there are
infinitely many functions to pick from, and messing with the one from
`complex_plot` didn't help in my first tries.
* The way the alpha is used is almost assuredly inefficient. Ideally we
would have a 'master list' of the roots and then one would search for one
of the n times 20 combinations of root and iteration level, and assign a
color to that from the 'master list' (dictionary?) instead of multiplying
by alpha 3 times for every single point!
* Probably the way I just slapped in a tuple for the new output of the
`which_root` is inefficient too - presumably one could at least define the
type coming out of it, if not find some better way to represent it.
* The exact (blue) circle in the picture, which is not flush with the
second iteration ellipse, probably indicates that the way the iterations
are determined is too aggressive/not aggressive enough (not sure which).
But it does work, and even looks somewhat decent. Can't compete with Java
yet, but it would be really nice to have this in Sage.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11837#comment:10>
Sage <http://www.sagemath.org>
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