Iterations of the C Curve

Various properties of finite iterations of the Lévy C curve, including coordinates, boundary, area, squares, centroid, moment of inertia, and weight in regions.

A C curve image (about 2 kbytes).

Read draft 5,

PDF c-curve.pdf (about 821k, 68 pages)
LaTeX source c-curve-5.tar.gz (about 888k, 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 more material to be added. The LaTeX source uses PGF for the pictures.

Document copyright 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022 Kevin Ryde. Permission is granted for anyone to make a copy for the purpose of reading it. 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. Some C code makes graphs for Nauty. The document has self-tests in Pari/GP and the functions there are extracted to a devel/c-curve-defines.gp which is highly specific to the document but might be of interest for experimenting. (Requires GP 2.9 up for some things.) A big Pari/GP file has generating functions for the various configuration counts.

See Math::PlanePath::CCurve for Perl code implementing curve coordinate calculations. The corresponding CCurve section of the PlanePath image gallery has some pictures. The PlanePath sources include an examples/c-curve-wx.pl program for interactive viewing (with wxPerl).