#12454: A draw_rauzy_fractal method for WordMorphism
-----------------------------+----------------------------------------------
Reporter: tjolivet | Owner: sage-combinat
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.0
Component: combinatorics | Keywords: rauzy fractal, substitution,
word morphism
Work_issues: | Upstream: N/A
Reviewer: vdelecroix | Author: tjolivet
Merged: | Dependencies:
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Comment(by vdelecroix):
> Replying to [comment:10 vdelecroix]:
> > 1) For the construction of colors, there is a built in functions
"rainbow" in sage.plot.colors (you can call it with 'rgbtuple' option).
>
> Yes, I'm aware of the rainbow function, but colormaps offers many color
schemes and it works fine, so I used it.
I see. Your way is definitely better.
> > 2) and 2')
It is now #12512. Could you replace your loop with either
{{{
u = iter(self.periodic_point(letter))
}}}
where letter is a parameter, or
{{{
u = iter(self.periodic_points()[0][0])
}}}
3) Why did you choose 1000 for the precision of the complex field ? It
seems a little bit big for your purpose. Won't you make it a parameter
(with a reasonable default value) ?
4) Why do you assume that the root is cubic ? On one hand, if they are
ordered as |l_1| > |l_2| > 1 > |l_3| then you will get a strange Rauzy
fractal, won't you ? On the other hand, I have examples for which the
absolute values of eigenvalues are ordered as |l_1| > |l_2| > 1 > |l_3| >
|l_4|. Then you can obtain a Rauzy fractal after a projection parallel to
v_1 and v_2 on the plane generated by v_3 and v_4 (where v_i is an
eigenvector associated to l_i). In other words, I'm a little bit confused
with your restrictions.
Otherwise, everything is very nice. You should now write a tutorial with
both methods for drawing Rauzy fractals with nice pictures and put it in
the documentation ;-)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12454#comment:12>
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