Simó's simple 3-body choreographies and their Fourier Transforms

Recently (to 3 December 2002, from my point of view) Carles Simó has released a new set of 3-body choreographies at They are obviously candidates for taking the Geometrical Fourier Transform. This page indexes the results of doing that. The technical difficulties involved in doing it, using Mathematica and starting from a large data file in a rather obscure GNUPlot format, are discussed elsewhere.

The files are just indexed with the numbering that Simo published them in, 1–345. They are grouped into blocks just because there are so many. The Moore-Chenciner-Montgomery solution is number 001. The 000 case is the Lagrange equilateral triangle solution. This page has just 50 thumbnails, namely numbers 00–049. For more, up to number 345, go to other blocks using the menu at the top of the page. Some of the orbits Simó has found are amazingly complex for periodic orbits with three equispaced (in time) bodies runnning around after each other.

Missing images suggest bugs in my processing or in my derived data files. For an explanation of the notation and coloring of the diagrams see the Guide under its button.

There are animated SVG forms of the images available, if you have a newer browser and have already, or are willing to, download the Adobe SVG Viewer Plugin, or some other viewer. [SVG (Scalable Vector Graphics) is a recommended XML markup for two-dimensional graphics coming from the W3C (World Wide Web Consortium), who bring us HTML, HTTP, XML, PNG, CCS, MathML, RDF and many other protocols for the Web.]

000 001 002 003 004
005 006 007 008 009
010 011 012 013 014
015 016 017 018 019
020 021 022 023 024
025 026 027 028 029
030 031 032 033 034
035 036 037 038 039
040 041 042 043 044
045 046 047 048 049