#E1523D

science:

Quasicrystals as sums of waves in the plane.

intothecontinuum:
Islamic Stars by Jim Bumgardner. Source code for Processing here. If you are running a browser which supports Java, then you can use your mouse to interact with the applet above.

Move the mouse horizontally and vertically to change the image. X and Y control two different parameters. This was an experiment with a method used to produce Arabic/Islamic star tiling patterns, from an underlying grid of polygons.

Starting with an underlying grid of polygons, the star pattern is produced by drawing lines from two equidistant points on each polygon edge at some fixed angle (controlled by the mouse). At the point where the lines would intersect with other lines, they are clipped. Y controls the distance from the center of the polygon edge.
X controls angle.

science:

Usually, when art and science, or science and religion, intersect, they are seen as being in opposition. Art is free-flowing where science is rigorous; religion is faith-based where science needs evidence. But sometimes, the three actually intersect in ways that, at least to my eye, actually heighten the beauty of all of them. One such example is medieval Muslim ornamentation.

Imagine you have a fixed set of tile shapes, but you can have as many of each as you want. Can you tile them in such a way that you fill an infinite plane, with no gaps? If you can, you’ve got yourself a tiling. If you can shift the pattern around in some way, say, one unit to the left, so that the end result is the same as you started with, you’ve got a periodic tiling. But if any shift at all in the pattern creates a unique pattern, the tiling is said to be non-periodic. And if you’ve got a set of tile shapes that can only form non-periodic tilings, no matter what pattern you make with them, the set of tiles is said to be aperiodic. Until the mid-20th century, mathematicians doubted that there could be aperiodic tilings. But in the 1970s, Roger Penrose discovered a set of very simple tiles that—if you apply a couple of restrictions to how they can be arranged (restrictions that can be made superfluous if you give the tiles some bumps)—are aperiodic, i.e., no matter how you arrange these tiles, and no matter how large a plane you tile, you will never find a periodic pattern. They’re called Penrose tiles.

This was new knowledge. No one knew about this until Western mathematics started exploring this in the mid-20th century. Or so we thought.

Because of Islam’s restrictions on religious iconography, such as depicting living beings, Islamic artists have found ways to make the most of abstract patterns and shapes. You see it in Arabic calligraphy, and you see it in the magnificent shapes on the walls of mosques and religious schools. In 2007, physicists Peter Lu and Paul Steinhardt discovered that the patterns on the walls of medieval Islamic buildings very closely resemble Penrose tilings. The crucial invention of girih tiles, basic shapes used to build more complex patterns, allowed Islamic architects to decorate their walls with non-periodic tilings. And in the Darb-e Imam shrine in Ishafan, Iran, built around 1450 (above), the tiles almost perfectly form a pattern that can be generalized as a Penrose tiling. If you deconstruct the pattern on the Darb-e Imam shrine into Penrose tiles, you’ll find that only 11 out of 3700 are mismatched, and the mismatch is so small that it’s “removable with a local rearrangement of a few tiles without affecting the rest of the pattern”. (more)

science:

Picture 1: wall mosaic on Darb-E Imam shrine (left) / atomic model of silver-aluminum quasicrystal (right). Picture 2: infographic from the Nobel Foundation.

This year’s Nobel Prize in chemistry was awarded to Dan Shechtman for his discovery of quasicrystals. Quasicrystals, unlike traditional crystals, are aperiodic on the atomic level. Basically, their patterns don’t repeat. When Shechtman first saw this in an experiment in 1982, this was scientific heresy. Crystals were periodic, period. Shechtman must have made a mistake. But he hadn’t, and rather than sitting around sulking about his doubtful colleagues, he worked hard to eliminate possible errors and build further evidence for the existence of quasicrystals. The tide of evidence turned in his favor, and the field of crystallography was changed forever.

In hindsight, quasicrystals are the sort of thing that seem to be too beautiful not to exist. (Which is not to say that, just because a theoretical structure is beautiful, it always turns out to exist—it doesn’t.) Although it took until 1982 to find evidence of atomic patterns that were not periodic, aperiodic tilings show up on the walls of mosques as early as the 12th century.

Nature in Ornament (1892)

Author: Day, Lewis Foreman, 1845-1910
Subject: Decoration and ornament; Nature (Aesthetics)
Publisher: London : B.T. Batsford ; New York : Charles Scribner’s sons

found: here

Pattern design : a book for students treating in a practical way of the anatomy, planning & evolution of repeated ornament (1915)

Author: Day, Lewis Foreman, 1845-1910
Subject: Design; Patternmaking; Decoration and ornament

found: here

Surficial pattern of receptaculitids (1969)
Author: Nitecki, Matthew H
Volume: Fieldiana, Geology, Vol.16, No.14
Subject: Dasycladaceae, Fossil
Publisher: [Chicago] : Field Museum of Natural History

found: here

Escher

via artmight.com

Escher

via artmight.com

Escher / twon Blowball

via artmight.com