Quasi-crystalline vitrail (2nd of March 2014)

Vitrail, blue and yellow

Ljubljana and Zagreb are neighbor cities. Zagreb is, when one thinks about it, a capital almost on the border, and Slovenia is small so that one reaches Ljubljana in no time. And the other way around. That is why I see >> Primož relatively often. For example yesterday, blowing off mandala while we were walking through Mirogoj cemetery.

But we hear each other, mostly professionally, even more often. That is why I very well know the whole story regarding Primož's last success. It concerns the publication of the paper >> "Mosaic two-lengthscale quasicrystals" in Nature which is probably the most important scientific journal. I couldn't be a part of the scientific story, but I engaged in the happening in the way I could, which is to try to represent the results by Dotera, Oshiro and Ziherl in a slightly different way - the one that is often required for cover pages of books and journals and in the texts popularizing science. The result is shown in the image above (a detail of that image is shown below).

Unfortunately, we didn't succeed in publishing the image on the cover of Nature, >> but we made it to Nature Physics, in a review of the work by Primož and coworkers written by Michael Engel and Sharon C. Glotzer entitled "A triangular affair". There appeared the illustration shown in the image above.

Vitrail, blue and yellow, detail

The paper by Primož and his coworkers deals with the formation of special phases of two-dimensional matter made of soft disks. The disks are soft in a special way, so that they have a soft outer rim and hard core. They can thus easily deform up to a certain extent when the hardness of their core stops further deformation.

The phases which arise depend on two length scales, which are set by the radius of the core and the disk radius (i.e. the thickness of the soft part of the disk). Primož and his coworkers have shown that, depending on the interplay of the two length scales, different types of two-dimensional "matter" arise - they have different symmetries and arrangement which one may call quasi-crystalline. This is where I will stop with my explanation of science and continue with visual aspect a little bit more.

Quasi-crystalline phases look like tilings of plane with rhombi, triangles and "holes", i.e. defects (the centers of soft disks coincide with vertices of rhombi and triangles). In the images above, rhombi and triangles are represented as pieces of blue and yellow glass, and the holes as pieces of almost fully transparent glass. All the shapes are mutually separated by a "copper wire" which is the only element of the visual representation of the quasi-crystal in the image below.

Vitrail, empty

The calculated shape was thus used to make something similar to a rosette or vitrail, and to enhance this representation even further, I used a "wooden" structure (above and below) which was also based on the calculations of Dotera, Oshiro and Ziherl. It was obtained from a two-dimensional Fourier transformation of the phases which Primož and his coworkers found, so that it represents an additional information on the ordering and structure of these phases.

Vitrail, empty, 3D

Of course, the shape is fully three-dimensional which can be seen in the image above.

The whole story is interesting also from another standpoint. On one hand, we have a central symmetry typical for church rosettes (wooden structure) and on the other, we have an aperiodic and rotationally non-symmetric finer pattern of copper wire, both patterns being harmonically superposed in the shape. But, unlike in Christian art, where such a geometry was not known so that my work represents a sort of a "sci-fi" modification of history, in Islamic art quasi-crystalline arrangement was known. I already wrote about it in the post on >> girih, which is now almost two years old.

Vitraj, red and green, detail
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Last updated on 2nd of March 2014.