Iterations of the Terdragon Curve

Various results on the terdragon curve, including coordinates, area, boundary, enclosure sequence, convex hull, centroid, moment of inertia, some trees, fractionals, and some results on the alternate terdragon curve.

A terdragon image (about 2 kbytes).

Read draft 15,

PDF terdragon.pdf (about 1217k, 124 pages)
LaTeX source terdragon-15.tar.gz (about 1287k, and sig)

Also by plain HTTP or by FTP or by RSYNC if desired. 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 the quality a little variable and more material to be added. Section numbers and theorem numbers will change. The LaTeX source uses PGF for the 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 generator and development programs which are all GPLv3 up. They're mostly Perl and a bit rough. The document has some self-tests in Pari/GP and its functions are extracted to a devel/terdragon-defines.gp which is highly specific to the document but might be of interest for experimenting.