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.

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.)

This page Copyright 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021 Kevin Ryde.