Posts tagged symmetry
An aperiodic monotile, sometimes called an “einstein”, is a shape that tiles the plane, but never periodically. In this paper we present the first true aperiodic monotile, a shape that forces aperiodicity through geometry alone, with no additional constraints applied via matching conditions. We prove that this shape, a polykite that we call “the hat”, must assemble into tilings based on a substitution system. The drawing above shows a patch of hats produced using a few rounds of substitution.
via https://cs.uwaterloo.ca/~csk/hat/
In the second edition of Where is Everybody? I discuss what Gerard Foschini calls the canonical artefact (TCA) — a flag for the presence of an advanced intelligent life-form. I don’t propose to discuss the details of TCA in this post — you can read the book if you’re interested — but I do want to provide an update. I was fairly sure that no-one had constructed an example of TCA, but yesterday Foschini emailed me a photo of it: he built it out of coin stacks with black rubber test tube stoppers as separators. Below, shown with gratitude, is Foschini’s TCA.
via http://stephenwebb.info/tag/canonical-artefact/
Deformed “Shasta daisy” in Nasushiobara City / 0.5 μSv/h at 1m above the ground (via https://twitter.com/san_kaido/status/603513371934130176)
Quasicrystals are groups of molecules bonded together in structures that resemble crystals in that they are organized, but unlike crystals, the structures are not nearly as uniform. In fact, they are quite the opposite—though they are locally symmetric, they lack any sort of long distance periodicity. Because of their chaotic nature, quasicrystals tend to feel slippery to the touch, which is why they have been used to coat the surface of non-stick frying pans. The first quasicrystal was made, also by accident, in 1982, by Daniel Shechtman (who later won a Nobel prize for his work). Since then many more of them have been made in various labs, (one was even found to exist in a meteorite) though most of them have had one thing in common, they were all formed from two or three metal alloys. In this latest discovery, the quasicrystals self-formed after the researchers placed a layer of iron containing molecules of ferrocenecarboxylic acid on top of a gold surface. The team was expecting to see a linear group of stable molecules pairing up as dimers, but instead were surprised to find that they had formed into five sided rosettes—it was the rosettes that pushed other molecules into bonding forming crystalline shapes, resulting in the formation of 2D quasicrystals that took the form of several different shapes: stars, boats, pentagons, rhombi, etc., all repeated in haphazard fashion.
http://phys.org/news/2014–03-group-quasicrystals.html
