#12454: A draw_rauzy_fractal method for WordMorphism
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Reporter: tjolivet | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: combinatorics | Keywords: rauzy fractal, substitution,
word morphism
Work_issues: | Upstream: N/A
Reviewer: | Author: tjolivet
Merged: | Dependencies:
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From the docstring:
Returns a plot of the Rauzy fractal associated with a substitution that
admits a real eigenvalue of degree 3. The substitution does not have to
be irreducible, and there are no restrictions on its alphabet.
plots with less than 500,000 points usually take less than 30 seconds, and
several millions of points can be plotted in reasonable time.
The definition used can be found found for example in [1]. The usual
definition of a Rauzy fractal requires that its dominant eigenvalue is a
Pisot number. The present code doesn't require this, allowing to plot some
interesting pictures in the non-Pisot case (see the examples below).
Other ways to draw Rauzy fractals (but less general) can be found in
``sage.combinat.words.paths.FiniteWordPath_3d.plot_projection`` or in
``sage.combinat.e_one_star``. (The former however allows to plot some 3D
Rauzy fractals associated with some quadratic Pisot numbers.)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12454>
Sage <http://www.sagemath.org>
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