Iterations of the R5 Dragon Curve

Various results on the R5 dragon curve, including coordinates, area, boundary, enclosure sequence, convex hull, centroid, moment of inertia, area trees, and some fractionals. Also some results on the quartet curve and tree which are a similar base.

A sample R5 dragon image (about 1.5 kbytes).

Read draft 11,

PDF r5dragon.pdf (about 1343k, 124 pages)
LaTeX source r5dragon-11.tar.gz (about 1512k, and sig)

Also by plain HTTP or by FTP or by RSYNC. The sig file is a Gnu PG ascii armoured signature generated from my key.

"Draft" here means believed correct as far as it goes but with variable quality and more to come. The LaTeX source uses PGF for pictures.

Document copyright 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021 Kevin Ryde. Permission is granted for anyone to make a copy for the purpose of reading it. Permission is granted for anyone to make a full complete verbatim copy, nothing added, nothing removed, nothing overlaid, for any purpose. The PDF rendition contains fonts which are Copyright American Mathematical Society and licensed under the Open Font License.

The source .tar.gz includes various generator and development programs which are all GPLv3 up. They're mostly Perl and a bit rough. Modules variously used include FLAT, Graph, and Math::Geometry::Planar (some debs in my repo). The document has self-tests with Pari/GP and my gp-inline. GP functions are extracted to a devel/r5dragon-defines.gp which is highly specific to the document but might be of interest for experimenting. (Needs GP 2.9 up for some things.)

See my Math::PlanePath modules R5DragonCurve and QuintetCurve for Perl code implementing curve coordinate calculations. The corresponding R5DragonCurve and QuintetCurve sections of the PlanePath image gallery have some pictures.

(And yes, "Quintet" in the module name QuintetCurve was a mistake for what Mandelbrot calls Quartet, even if quintet may better hint at the base-5 nature.)