#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 slabbe):
* cc: slabbe (added)
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. 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) !
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) !
--
Comment:
I add myself in cc because I am interested.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8431#comment:3>
Sage <http://www.sagemath.org>
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