Iterations of the Alternate Paperfolding Curve

Various properties of finite iterations of the alternate paperfolding curve, including coordinates, boundary, area, Golay-Rudin-Shapiro sequence, twin alternate, area tree, and some fractionals.

A sample alternate paperfolding image (about 1.5 kbytes).

Read draft 13,

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 variable quality in places and more to come. Sections and equations will renumber. The LaTeX source uses PGF for pictures.

Document copyright 2016, 2017, 2018, 2019, 2020 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 and its interface to GPC. See my repo for some debs. The document has self-tests with Pari/GP and my gp-inline. GP functions are extracted to a devel/ which is highly specific to the document but might be of interest for experimenting. (Probably needs GP 2.9 up in places.) Some C code using the Nauty library makes alternate paperfolding curve graphs and trees for experimenting.

See Math::PlanePath::AlternatePaper for Perl code implementing curve coordinate calculations. The corresponding AlternatePaper section of the PlanePath image gallery has some pictures.

See Graph::Maker::TwinAlternateAreaTree for Perl code creating the area tree with (or similar).

This page Copyright 2017, 2018, 2019, 2020 Kevin Ryde.

(Back to the sitemap.)