This code runs the Mapper algorithm, developed by Gurjeet Singh, Facundo Mémoli, and Gunnar Carlsson, on a knot being rendered in Rob Scharein's software KnotPlot.
The code uses projection to the
usage: buy Knotplot. download this code. put it in KnotPlot, then load your favorite knot or link. run the following command:
lua run knotmapper/knotmapper.lua [number of bins] [percent overlap]
You'll get a graph6 representation of the resulting graph. Try using Mathematica to decode it while I write something in Lua to do it.
Examples:
Example link generated using the celtic lua
demo in KnotPlot.
Mapper output using 15 bins with 15% overlap, rendered with Mathematica. Note the graph has nine connected components and the knot has 9 strands.
Mapper output using 15 bins with 75% overlap, also rendered with Mathematica. A little noisier, but kind of vaguely the same.