Iterations of the Alternate Paperfolding Curve

Abstract: Various properties of finite iterations of the alternate paperfolding curve, including coordinates, boundary, area, twin alternate, area tree, and some fractionals.

A sample alternate paperfolding image (about 1.5 kbytes).

Read draft 5,

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 in places and more to come. The LaTeX source uses PGF for pictures.

Document copyright 2016, 2017 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. Modules variously used include FLAT and Graph (some debs in my repo). The document has self-tests with Pari/GP and my gp-inline. GP functions are extracted to a devel/alternate-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 Math::PlanePath::AlternatePaper for Perl code implementing curve coordinate calculations. The corresponding AlternatePaper section of the PlanePath image gallery has some pictures.


This page Copyright 2017 Kevin Ryde.

(Back to the sitemap.)