Tuesday, February 27, 2007

Snow sculptures from Breckenridge

Lately, we published snow sculpture by Bathsheba Grossman which was represented at Breckenridge snow sculpture contest. Here some other mathematical snow sculptures represented at Breckenridge in other years.

Knot divided (2005)

This is a triply twisted Moebius band. There is a self-referential beauty in our sculpture: If one forms a Moebius band by twisting a belt through three half-turns (instead of just one), then the band's edge forms a trefoil knot.

Whirled White Web (2003)

This sculpture is a 3-fold symmetrical whirl of twisted and stretched saddle shapes. Such saddles occur naturally in soap films that are spanning warped wire frames; such "minimal surfaces" are nature's way of creating strength in delicate structures. Our sculpture uses these natural ideas to create an intricate network of ribs and internal spaces suspended from a web of three mutually interwoven double loops.

Turning a Snowball Inside Out (2004)

In the 1960s, mathematicians showed how to turn a sphere inside out. To do this, the surface must pass through itself, but no tears or creases are allowed to form at any point. This design is an artistic interpretation of the halfway point of such a sphere-everting process, where the surface displays half of its outside, shown as a solid form, as well as half of its inside, rendered as a transparent grid.

Here we see a snail shell but it's also a representation of fractal twisting to it's center.

This article was created by materials of
http://www.cs.berkeley.edu/~sequin/SCULPTS/sculpts.html

Monday, February 26, 2007

Graffiti in Barcelona

Graffiti in Barcelona
Rosa y Dany
In this wonderful illustration we see the same artistic effect which Escher used in his lithograph "Reptiles" where reptiles go from tessellated surface of table into three-dimensional environment, crawl by things on the table and returns into tessellated surface. Unlike, Escher's artwork here reptiles appears from mosaic.

Wednesday, February 21, 2007

Fractals in nature

Fractals are not only mathematical abstraction, which can be used for creation of abstract or realistic images (see images by Keith Mackay). They can be found in our world in various plants, shells etc. Below you can see several examples of fractals in nature.

The most known fractal is fern leaf. Every little leaf of fern repeats whole large leaf.

Another interesting nature fractal is romanesco cauliflower, which is a cross between broccoli and Cauliflower, which accentuates the great fractal spiral patterns on the top.
In cactus below leafs become twisted towards the center.

Fractals also exists in micro world. Viruses, mould and bacterial aggregate colonies spontaneously assume fractal shapes.

The best known fractal representation among animals is nautilus shell.


Lightning Strikes and Electrical Discharge creates fractal formations called Lichtenberg figures on rocks, grass,wood or even people!
Many symmetrical wonderful fractal shapes can be found in snowflakes.


This post was created by materials of
http://www.its.caltech.edu/~atomic/snowcrystals/
http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html

Tuesday, February 20, 2007

Temperal paradox

Temperal Paradox
Patrick's Picks

After mystery of blank spot in Escher's lithograph "Print Gallery" was revealed many derived images have appeared. Very often these images are created from real photos as it was done in Stanford University with photo of Hendrik Lenstra who revealed the mystery.

The image above was created by Patricks Picks from photo of clock face. He also created many other similar images. You can see them in his profile on Flickr or in Escher's Droste Print Gallery pool.

Monday, February 19, 2007

Dog Dream

Dog Dream

In this artwork created by Kaz Maslanka we can see artistic representation of fractal like Koch snowflake.

The inscription at the top is in Korean:
Dog Dream = Irrationality / Importance