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If the sheep animation by Cyriak was too creepy for you, check out his work with isometric fractals on this music video for the song “True Loves” (Cereal Spiller Remix) by Hooray For Earth. -via The Daily What
The following is an article from the science humor magazine Annals of Improbable Research.
Note how the bottom of the Grand Canyon (in this rare view) is darker than at the top, giving an idea of how solar radiation attenuates the deeper one goes into the canyon. (Image credit: Wikipedia user chensiyuan)
By Earle E. Spamer
American Philosophical Society, Philadelphia, Pennsylvania
For a long time now, people visiting the Grand Canyon of the Colorado River have been told it is about 12 to 18 miles wide and “more than” a mile deep, convinced that its majestic views are due to the incessant powers of erosion. New analyses now indicate that the canyon is far larger than imagined. It can never be accurately measured and may unexpectedly hold the answers to long-held geological and environmental mysteries.
Fooling Some of the People
In 1903, President Theodore Roosevelt was the first to recognize generally that there was a problem with the Grand Canyon. Speaking near the canyon rim, he urged Americans to “keep it as it is.” He foresaw an endangered canyon, one that without our intervention would deliver a dwindled heritage to the “children’s children” of his audience. His plea, though widely repeated, went unheeded for decades.
Twenty years ago I devised a plan to place the Grand Canyon in stasis, until such time that the problem of erosion can be remedied. The Final Report1 called for filling the canyon with styrofoam packing material, or “piffles”—some 291 quadrillion of them, to be precise. This plan was also promoted by Grand Canyon National Park.2 I was interviewed a number of times for newspapers and radio to explain myself, and Internet features have taken up the cause.3 A few years later, my Further Final Report4 revealed that the plan had failed because, by mistake, biodegradable piffles had been used—at least, that was the conclusion. This was not correct.
The follow-up report went on to recommend that to safeguard an unprotected canyon, we should ensure that it not be visited at all, nor written about, nor photographed. I argued that all available superlatives have been overextended, and that the number of photons removed from the national park in tourist’s cameras have reached alarming numbers, greatly reducing the amount available for appreciation by our own children’s children. It would be pointless for most of us to visit the canyon anyway. It has been pre-appreciated for us, professionally, by celebrated writers, poets, singers, painters, photographers and filmmakers; our amateur efforts would be lacklustrously insufficient, depreciating further the superlatives and photons.
Still later I postulated that the Grand Canyon may be a fake.5 Had we been all along deceived about the identity or location of the canyon? Hundreds of other places around the world— and on other worlds—claim to be a (or the) Grand Canyon.6 I charged readers to campaign, vigorously, to have the “one true Grand Canyon” designated as the Official Grand Canyon. Apparently, our representatives in Congress and the editors of the world’s great newspapers have thought otherwise, ignoring the pleas of constituents and readers.
Straight Down to China
Now there is conclusive evidence to show that the Grand Canyon is not a fake. Rather, we have deluded ourselves into believing that it is disappearing due to erosion, when in fact it is far more immense than supposed. We have accumulated the evidence for a century and more, but have failed to recognize its significance.
more …
Vi Hart calls herself a “recreational mathemusician”, which sounds like fun! In this video, she teaches more about math than she missed by doodling during class. See more of this sort of thing at her website. Link -Thanks, David Israel!
A fractal is a fragmented geometric shape that, when split into parts, each part is roughly a smaller copy of the whole, a property called self-similarity. And it makes some damn wild images when you start injecting color, layers or even candy.
Benoit Mandelbrot, the French mathematician who is known as the father of fractal geometry, died last week. Good has posted a slideshow in his honor.
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This Koch snowflake cupcake is the tastiest mathematical iteration ever. These lovely fondant fractals are made from edible dough rolled, cut to exacting detail and assembled on top of the cupcake of your choice. Warning: some manual dexterity required.
The interesting thing about fractals like these is that they are emergent phenomena– complex patterns that show up when a simple algorithm is iterated. We often think of mathematical iteration as something that only happens in computers, but as these examples show, there are a number of interesting certain cases where you can perform iteration with your hands as well.
Link – Via RealityCarnival
Comments Off For many of us, the first time we appreciated the art of math was when we played with a Spirograph. However, it’s a long way from addition and subtraction to epicycloids, and very few of us actually study math that far. But those who do sometimes end up creating some very beautiful artworks based on mathematics and geometry.
Sculpture
Sculptor Bathsheba Grossman creates metal and crystal artworks of forms found in math, physics, biology, and astronomy. Grossmen shows us Borromean rings, hypercubes, gyroids, fractals, Calabi-Yau spaces, and interlaced sculptures based on the five Platonic solids. I particularly like this Voronoi network wrapped onto a Möbius toroid, sculpted in white glass.
Grossman created this beautiful lamp from one of her Ora series sculptures. Available in several lamp styles from Materialise.
Jewelry
The Julia set is a fractal equation that produces a series of rather pleasing spirals. Designer Marc Newson took that fractal shape and designed a necklace of 2,000 diamonds and sapphires that took jewelry craftsmen 1,500 hours to put together. Note that the necklace is not symmetrical, but still has a sense of balance. See how the jeweler, Boucheron, advertises the necklace.
Drawing
Probably the best known artist to use math concepts in his works is M.C. Escher. Many of his 2-dimensional drawings turned 3-dimensional geometry on its head. The lithograph titled Waterfall illustrates the concept of the Penrose triangle, also called the impossible triangle. Escher also explored tessellations in many of his drawings.
Computer Imaging
Paul Nylander was one of the developers of the Mandelbulb that we saw in a previous math post. He is a computer engineer and an artist who renders math and science concepts into colorful images including animated .gifs to help us visualize their 3- or 4-dimensional structures. Shown is a Dodeca-Spidroball, a variation on the spidron, which was invented by Daniel Erdely in 1979.
Belgian mechanical engineer Jos Leys renders and animates all kinds of math concepts into beautiful forms that boggle the mind. His artworks include fractals, Kleinian groups, inversive geometry, recursions, tessellations, knots, and tilings in both images and video renderings to show 3- and 4-dimensional effects. The image above is called Indra200, an example of “Kleinian jewelry“.
Other artists rendering math images worth checking out include Torolf Sauermann, Brian Johnston, Mehrdad Garousi, and the late Titia Van Beugen.
Video
Creating visual representations of math concepts became easier with computer rendering software and digital video capabilities. That doesn’t mean it is simple. Homporgo, the artist who created this video of a Mandelbox zoom said in a comment:
Believe me Bill, I wanted to go further too, but at the end part a single frame took 18 minutes to render, and the whole 1:27 minute video needed 12 days nonstop rendering. I felt thats more than enough at the time.
Twelve days! The result looks worth it to me. How about you? See more fractals on video in this post.
Previously at Neatorama: A Non-Math Look at Math Objects and A Non-Math Look at Math Shapes.
Make your own fractals with just a mouseover on these magic dots. Other interactive toys on the same site are just as fascinating, or should I say, addicting. Link -via Gorilla Mask
