#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 SimonKing):
I have attached
[attachment:newton_basins_with_iterations_and_double.spyx.txt]. I am sorry
that I have not been aware of Windows' automatic name extension (I don't
usually write texts under windows), and also I hope that it did not use
any fancy format.
Also I just noticed that the first line of the file contains %cython - of
course that needs to be removed if you want to attach it.
Anyway. The trick is to define `self.cutoff = 4./9`, and to use a
temporary `cdef ComplexDoubleElement diff = varia._sub_(root)`, so that
`(diff._complex.dat[0]**2 + diff._complex.dat[1]**2) < self.cutoff` is
fairly cheap.
Here are the data on sagenb:
{{{
%time
basin_plot([-1,1,3],(-.2,.1),(-.1,.1),plot_points=1000,figsize=7)
CPU time: 15.59 s, Wall time: 15.60 s
}}}
The same computation with the first "iteration" code takes `CPU time:
24.15 s, Wall time: 24.17 s`.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11837#comment:15>
Sage <http://www.sagemath.org>
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