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.
She starts with a clip that’s been digitally altered to sound like jibberish. On first listen, to my ears, it was entirely meaningless. Next, Das plays the original, unaltered clip: a woman’s voice saying, “The Constitution Center is at the next stop.” Then we hear the jibberish clip again, and woven inside what had sounded like nonsense, we hear “The Constitution Center is at the next stop.” The point is: When our brains know what to expect to hear, they do, even if, in reality, it is impossible. Not one person could decipher that clip without knowing what they were hearing, but with the prompt, it’s impossible not to hear the message in the jibberish. This is a wonderful audio illusion.
The central tension in camouflage is between being seen, and going unseen. With the discussion about what it is that constitutes national identity currently even being debated as part of the formation negotiations for the new Dutch coalition government, the core irony of this project looks to remain relevant for quite some time. If a Dutch identity exists, how would a camouflage for it function? Or more importantly, why would anyone want or need to conceal themselves with it in the first place? What you are hiding from? How you want to be seen?
If you want to get a rough grasp of how the leopard might get its spots, then building a CA model (or something similar) can be very illuminating. It will not tell you whether that’s actually how it works. This is an important example, because there is a classic theory of biological pattern formation, or morphogenesis, first formulated by Turing in the 1950s, which lends itself very easily to modeling in CAs, and with a little fine-tuning produces things which look like animal coats, butterfly wings, etc., etc. The problem is that there is absolutely no reason to think that’s how those patterns actually form; no one has identified even a single pair of Turing morphogens, despite decades of searching. [See “Update, 4 March 2012” below.] Indeed, the more the biologists unravel the actual mechanisms of morphogenesis, the more complicated and inelegant (but reliable) it looks. If, however, you think you have explained why leopards are spotted after coming up with a toy model that produces spots, it will not occur to you to ask why leopards have spots but polar bears do not, which is to say that you will simply be blind to the whole problem of biological adaptation.
Popping peyote buttons with his assistant in the laboratory, Klüver noticed the repeating geometric shapes in mescaline-induced hallucinations and classified them into four types, which he called form constants: tunnels and funnels, spirals, lattices including honeycombs and triangles, and cobwebs. In the 1970s the mathematicians Jack D. Cowan and G. Bard Ermentrout used Klüver’s classification to build a theory describing what is going on in our brain when it tricks us into believing that we are seeing geometric patterns. Their theory has since been elaborated by other scientists, including Paul Bressloff, Professor of Mathematical and Computational Neuroscience at the newly established Oxford Centre for Collaborative Applied Mathematics.
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.
“It’s not the subject of calculus as formally taught in college,” Droujkova notes. “But before we get there, we want to have hands-on, grounded, metaphoric play. At the free play level, you are learning in a very fundamental way—you really own your concept, mentally, physically, emotionally, culturally.” This approach “gives you deep roots, so the canopy of the high abstraction does not wither. What is learned without play is qualitatively different. It helps with test taking and mundane exercises, but it does nothing for logical thinking and problem solving. These things are separate, and you can’t get here from there.”
By and large, graphic design students bring a laptop to school, and create their work using digital software tools. This hard- and software represent a technological and cultural heritage that is seldomly questioned, and a potential that goes unexploited. Using free and open source software and engaging in its culture provides an alternative by making a design practice possible with a more intimate and experimental relation to its toolbox. Beyond the implications for design practice, the culture of free and open source software challenges traditional education paradigms because knowledge is exchanged outside institutional borders, and participants move between roles easily (teacher, student, developer, user). Following from their series of workshops and Print Parties, OSP proposes a summer school experiment. A first try to move across the conventional school model towards a space where the relationship to learning is mediated by graphical software.
Examples of catastrophic and systemic changes have been gathering in a variety of fields, typically in specialized contexts with little cross-connection. Only recently have we begun to look for generic patterns in the web of linked causes and effects that puts disparate events into a common framework—a framework that operates on a sufficiently high level to include geologic climate shifts, epileptic seizures, market and fishery crashes, and rapid shifts from healthy ecosystems to biological deserts. The main themes of this framework are twofold: First, they are all complex systems of interconnected and interdependent parts. Second, they are nonlinear, non-equilibrium systems that can undergo rapid and drastic state changes.
