#8431: Rauzy fractal (discrete planes and broken lines)
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Reporter: vdelecroix | Owner: vdelecroix
Type: task | Status: new
Priority: major | Milestone: sage-4.3.4
Component: combinatorics | Keywords: word morphism
Author: vdelecroix, sstarosta | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by vdelecroix):
* type: defect => task
Old description:
> Thinking about it for a long time and motivated
> by [http://trac.sagemath.org/sage_trac/ticket/8423&usg=AFQjCNG8_y-
> UlT3ON3unoD3utIEHQfTYbQ| #8423] this ticket stands for
> * the creation of WordMorphismExtension and WordMorphismExtensionDual
> (from [http://iml.univ-mrs.fr/~arnoux/AISrev.pdf|an article of Sano-
> Arnoux-Ito])
> * think about easy to use functions for plotting Rauzy fractals using
> those algebraic tools
New description:
Thinking about it for a long time and motivated
by [http://trac.sagemath.org/sage_trac/ticket/8423&usg=AFQjCNG8_y-
UlT3ON3unoD3utIEHQfTYbQ| #8423] this ticket stands for
* the creation of WordMorphismExtension and WordMorphismExtensionDual
(from [http://iml.univ-mrs.fr/~arnoux/AISrev.pdf|an article of Sano-
Arnoux-Ito])
* think about easy to use functions for plotting Rauzy fractals using
those algebraic tools. The broken lines and their projection for
WordMorphismExtension and discrete planes approximation from
WordMorphismExtensionDual.
We could be able to access the extensions as a method of morphisms
{{{
sage: s = WordMorphism('a->ab,b->ac,c->a')
sage: s.extension()
Word morphism Extension [...]
sage: s.extension_dual()
Word morphism dual extension [...]
}}}
And plot them easily from fractals.
{{{
sage: s = WordMorphism('a->ab,b->ac,c->a')
sage: fractals.RauzyFractal(morphism=s, format='broken_line')
sage: fractals.RauzyFractal(morphism=s, format='discrete_plane')
}}}
The algebra requires the creation of few other classes which
* Face and Patch (which is union of faces)
* WordMorphismExtension and its dual
* WordMorphismExtensionIterations for plotting approximations of the
limit fractal from the extension or its dual
TODO: think about cython for having fast data structure for Face and Patch
(which heritates from tuple and set) !
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8431#comment:2>
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