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Murilo

Around this time 2 years ago I was reading an article about protein folding in order to generate single line plane filling curves. The inspiration came from Ani Albers meandering lines.

gallery.bananabanana.me/p5js/a

Secondary Structures in Long Compact Polymers Richard Oberdorf!, Allison Ferguson!, Jesper L. Jacobsen??, and Jané Kondev' ! Department of Physics, Brandeis University, Waltham, MA 02454, USA 2LPTMS, Université Paris-Sud, Bdtiment 100, 91405 Orsay, France and 3Service de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France (Dated: February 2, 2008) Compact polymers are self-avoiding random walks which visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations. We present a Monte-Carlo algorithm which uniformly samples compact polymer configurations in an efficient manner allowing investigations of chains much longer than previously studied. Chain configurations generated by the algorithm are used to compute statistics of secondary structures in compact polymers. We determine the fraction of monomers participating in secondary structures, and show that it is self averaging in the long chain limit and strictly less than one. Comparison with results for lattice models of open polymer chains shows that compact chains are significantly more likely to form secondary structure. Murilo: "Sure."
Fig 1: Compact polymer configuration on a 6 x6 lattice. This “plough” configuration is used as the initial state for the Monte-Carlo process.
FIG. 2: Illustration of the "backbite" move used to generate a new Hamiltonian walk from an initial one. Starting from a valid walk a), one additional step is made starting at either of the two ends of the walk, b). Next we delete a step, shown in c), to produce a new valid walk, d).
Image of a single line space filling curve generated with the method described in the article.
Murilo

I have also printed this in a variety of formats and colors with a pen plotter!

Picture of a single line space filling curve printed in pink on a white file paper.
Picture of an Axidraw pen plotter printing a single line space filling curve with a ballpoint pen (those with 4 colors) on white file paper.
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