Archive for the ‘week2_math’ Category

Week 2-Mathematics,Perspective,Time,Space-Gindy Nagabayashi

Sunday, January 25th, 2009

This week’s topic was enlightening for me as I was reminded that math and art go hand in hand. After perusing through the featured links, the one the captured my attention was “Pollock’s Fractals”. Jackson Pollock’s famous drip paint artwork captivated many due to the fractal dimensions that closely resemble those found in nature. Pollock’s work may appear simple but in fact his artwork was so successful because of the subtle complexity.

The article mentions Pollock’s last drip painting “Blue Poles”. This painting reminds me of the shadow of a forest. The meshing of the many colors are striking and appear as though they are dancing of the wall. I found fractals especially interesting because of the optical illusion that the images play on mind, and best treat was the article tying together the idea of fractals with the artwork of Pollock. http://www.smh.com.au/ffximage/2007/11/30/BluePoles_wideweb__470×236,0.jpg

On another note, this week’s topic reminded me of the art of Julian Beever, an artist whose medium is the pavement. He uses perspective to create three dimensional pavement drawings. Beever’s artwork must be viewed at specific angles. Perspective is critical for his drawings to be so realistic.

http://users.skynet.be/J.Beever/images/fountain.jpg

If viewed from the wrong angle, the image looks distorted.

http://polizeros.com/wp-content/uploads/2006/03/julian-beever.jpg

http://www.cbsnews.com/stories/2008/03/02/sunday/main3897559.shtml.

Overall I thoroughly enjoyed “Mathematics, Perspective, Time, and Space”. Initially was not looking forward to the topics because the idea of mathematics in art did not seem to connect. Art and mathematics are completely complementary.

week2 \ relevant links \ Alberto Pepe

Thursday, January 22nd, 2009

http://cornelius1.com/blog/uploads/800px-Fibonacci_spiral.svg.png
http://upload.wikimedia.org/wikipedia/commons/0/0a/The_Great_Wave_off_Kanagawa.jpg
http://www.3d-digital-graphic-art.com/page-multiple-vanishing-points1-tutorial.html
http://www.youtube.com/watch?v=zIZcl8q0u4Q
http://agutie.homestead.com/Files/escher/escher_circle_limit_1.html
http://www.d.umn.edu/~ddunham/dunham.am.pdf
http://seedmagazine.com/news/2008/07/the_shape_of_music.php
http://www.seedmagazine.com/news/2009/01/painting_and_the_pleistocene_1.php
http://www.superliminal.com/fractals/bbrot/bbrot.htm
http://www.youtube.com/watch?v=nBXqnN7vNzk&feature=related
http://www.youtube.com/watch?v=5ej3dj4×64k
http://www.paikstudios.com/
http://en.wikipedia.org/wiki/Julian_Beever
http://www.strangehorizons.com/2002/20020916/fourth_dimension.shtml
http://www.hiddendimension.com/Mathematics_Main.html
http://www.youtube.com/user/stupidjaguar7
http://209.85.173.132/search?q=cache:UCLHpqiaYkkJ:press.lacaixa.es/socialprojects/show_annex.html%3Fid%3D2618+Escher%27s+shape+of+life&hl=en&ct=clnk&cd=1&gl=us
http://www.youtube.com/watch?v=uk2sPl_Z7ZU
http://www.generatorx.no/
http://flickr.com/groups/generatorx/
http://www.youtube.com/watch?v=wH6-twlgJhU
http://www.youtube.com/watch?v=1AZe9g2Huz0
http://plus.maths.org/issue8/features/art/
http://www.cs.berkeley.edu/~sequin/SCULPTS/LONGHURST/
http://www.susqu.edu/Art_Gallery/Exhibitions/Ries-Sep1999/Ries.jpg
http://tonyrobbin.home.att.net/work.htm
http://www.cc.gatech.edu/home/idris/Stories/Einsteins_Dreams.htm
http://www.dartmouth.edu/~matc/math5.geometry/unit16/unit16.html

Week 2/ Hokusai/ Patrick Morales

Wednesday, January 21st, 2009

On my search for more wave art after being inspired by Reuben Margolin’s wave installations I stumbled upon Katsushika Hokusai’s most famous woodblock print.  The Great Wave off Kanagawa represents the rage and chaos of an ocean storm in a contained and clean depiction.  I learned that Hokusai used various mathematical elements to create the print.  The waves are based on circles and Mount Fuji is based on a triangle.  The threatening fingers of the wave are fractal-like.  Even the general shape of the wave is somewhat reminiscent of the Fibonacci spiral.   The print is an excellent example of how a moment dominated by motion is captured in still art.  The whole subject of math being utilized in art fascinates me because it makes one ask the question: is one appreciating art or math?  It is completely plausible for one to answer that we are enjoying both at the same time.

Fibonacci Spiral
http://cornelius1.com/blog/uploads/800px-Fibonacci_spiral.svg.png

The Great Wave off Kanagawa by Katsushika Hokusai
http://upload.wikimedia.org/wikipedia/commons/0/0a/The_Great_Wave_off_Kanagawa.jpg

Last year in AP Art, while studying vanishing points, I attempted to create a picture with infinitely many vanishing points.  What I ended up with was frustration and a mad art teacher who had told me I was wasting my time from the beginning.  Thanks to my juvenile but hilarious endeavor I now understand that perspective is very complex, the picture of FIVE vanishing points still rattles my brain.  I began studying illusions created by perspective and vanishing points.  I think a study of  perspective can quickly transform itself into an interest in the different dimensions of reality.  The video about 10 dimensions that was shown in class was based on a linear perspective of infinity and time, it being the only perspective that humans know.

Vanishing Points
http://www.3d-digital-graphic-art.com/page-multiple-vanishing-points1-tutorial.html

Paper Dragon Illusion
http://www.youtube.com/watch?v=zIZcl8q0u4Q

Week 2/The Fourth Dimension/Joseph Racca

Tuesday, January 20th, 2009

The Concept of Zero and the Fourth Dimension

The power of zero: although in math, we see zero as the symbol that represents nothing, zero is a powerful number, well actually, not just as a number but as a symbol.  when accompanied by one, zero can make that one into ten, one hundred, or one million, etc.

When dealing with the symbol zero, we are yet again torn between two views.  Similar to the differing views of art and science, art as a science or science as an art, the concept of zero is also observed and interpreted in many ways.  For example, in lecture, Professor Vesna mentioned that zero has been ever changing, with a different meaning with each coming culture/civilization:

“Some historians favor the explanation that it is omicron, the first letter of the Greek word for nothing –”ouden”.”

“During the Middle Ages, zero was disparaged as a mark of infidel sorcery, the sign of the Devil himself [. . .] ”

“For the Mayans, Zero was the Death God”

“Only much later was zero reinterpreted as a symbol of God’s power to create a lot out of naught.”

From a symbol representing certain gods, to a symbol that represents nothing, it brings me to continue exploring the concept of zero, as we see it today.  We see zero as the value for nothing. In math, 1 minus 1 equals zero, in art the vanishing point is used as a point to where we can no longer see anything, we can call it the point of zero if you will.

In considering zero, it brings me to the question and gets me thinking about what nothing is.  In science, how do scientists explain nothingness?  I’ve heard that black holes suck up objects that are in their paths and leave nothing behind.  But in art, how does an visual artist interpret and convey nothingness?  Would it be a color or would it be an abstract piece?

In “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusuion,” Henderson states that Dominguez recognized time as the primary definition of the fourth dimension.  So that leads to the question: Does time exist when nothing is present or does time just stand still?  According to Robbin and his view of the fourth dimension, it all depends on how we look at things.  “[Artists] are motivated by a desire to complete [their] subjective experience by inventing new aesthetic and conceptual capabilities.”  However, scientists, according to Robbin, “[work] simultaneously on a metaphor for space in which paradoxical three dimensional experiences are resolved only by a four dimensional space.”

So basically, in the concept of the “fourth dimension” people express their views.  This is what fourth dimension aims to uphold–a space for people to find their own perspectives, and look at things in new ways, new perspectives, which in the end leads to new ideas, concepts, inventions, and expression in both in the world of art and of science .

http://www.house2homeideas.com/images3/VWNUM0.jpg

http://farm4.static.flickr.com/3062/2696690900_48043390dd.jpg?v=0

Week 2/ Finding Logic in the Art/ Tammy Le

Monday, January 19th, 2009

Sometimes some art pieces seem so abstract that all the audience precieves is chaos on a canvas and disregards the thought and processes that an artist integrates within the piece, leaving many artists and their masterpieces unappreciated by viewers who cannot understand the logistics needed in creating such art.  When we first looked at Jackson Pollock’s Fractals, I was confused and lost as to its importance and could not recognize how Pollock demonstrates the mastery of his craft.  My perception of his work, however, changed once I learned of the complexity involved in creating his seemingly simple drip paintings.

Although what audiences precieve is merely patterns, shapes, and colors entangled within eachother, they barrier that divides art and math into seperate realms is broken down as geometry plays a key role in Pollock’s fractals.  Fractals are geometric shapes and patterns that can be split into parts, each of which is a different magnification of the whole, a property called self-similarity. Stemming beyond merely fractals using mathematical elements, Pollocks fractals show connections between more than just math and art, and adds a  biological component also.  Some of his artwork can showcase irregular yet patterned shapes in our natural environment such as tree branches, lightening, clouds, and mountains.  In discussing the importance of the correlation between math and art, how both can reflect nature is just as important, and Pollocks fractals showcases how all three can be interconnected and illustrated through a mere painting.

Mathematicians began studying fractals and their elements in the 1860’s and for a century they referrered to such shapes as “pathological monsters” because they could not find a connection between fractals and nature.  It was assumed that the complexity of natural objects, such as coastlines and clouds, was a result of pure disorder, unlike the sytematic pattern repetition that the mathematical view toward fractals presented.  The connection between fractals and nature began to be recognized in the 1960’s and 70’s when Benoit Mandelbrot’s “The Fractal Geometry of Nature” was published, revealing that the complexity of many elements of nature were shown to be the result of fractal repetition.

Here is an example of the connection between fractals and nature that can be related to Pollock’s work:


Pollock’s signature use of fractals allows his work to be easily recognizable and authenticated by physicists and mathematicians.  His mastery of the use of the mathematical element of fractals is difficult to match by imitators.  It is more than random patterns of splattered paint, but in intricate systematic composition.  Fractals have varying degrees of complexity on scales ranging from 0 to 3 where “One-dimensional fractals (such as a segmented line) typically rank between 0.1 and 0.9, two-dimensional fractals (such as a shadow thrown by a cloud) between 1.1 and 1.9, and three-dimensional fractals (such as a mountain) between 2.1 and 2.9.” Understanding the mathematical complexity behind Pollock’s work adds another dimension of imagination and creativity to the piece.  It leaves more audiences in awe of the spectacle before their eyes as they try to understand and uncover the logistics behind pieces such as Pollocks Blue Poles:

The painting becomes more than just aesthetics on a canvas and gives a glimpse into the harmony between art and mathematics that few are able to capture and preserve for the world to see like Jackson Pollock.

Once the mathematical complexity behind his work was recognized, other artists stopped claiming  “splatter boards were better than Pollock’s work” and began to celebrate him as an incredible artist and an icon in the art world.  As Desma 9 progesses throughout the quarter, I feel my view towards art that I did not understand before will continue to change and my appreciation of the skill and imagination it takes to incorporate science and art will contribute to a growing appreciation for art and the world as a whole.

Week 2\The Fourth-Dimension\Marian Portugal

Monday, January 19th, 2009

I never realized that art contains so much math and geometry until week two’s lecture on Tuesday.  Watching Youtube videos and getting to see several examples of these works of art helped me understand the connection math and art have with each other.  In Linda Dalrymple Henderson’s article, The Fourth Dimension and Non-Euclidean Geometry in Modern Art:  Conclusion, Henderson talks about the fourth dimension, which includes more elements such as time, space, and motion. 

One of the art projects that I thought related to the fourth dimension was M.C. Escher’s Circle Limit III.  Circle Limit III relies heavily on mathematics in order to create its desired effect.  Escher’s inspiration for this project came from a mathematician, H.S.M. Coxeter.  After its completion, Coxeter mentioned that Escher’s Circle Limit III, which contains hyperbolic tessellations, accomplished mathematical perfection, in which his calculations were correct to the millimeter.  Not only does this work of art contain mathematical elements, but it also has elements of space.  As your eye moves from the center to the outside of the circle, the fish get smaller, but still maintains its pattern.  With the fish getting smaller and smaller, it gives the illusion of looking through a convex lens, thus providing a multi dimensional view on a two-dimensional flat plane. 

Another piece of art that I believe is a product of mathematics, perspective, time, and space are kaleidoscopes.  A kaleidoscope consists of a tube, mirrors, and small objects.  Henderson’s article mentions that Duchamp, an artist, added shadows, mirrors, and virtual images to the four-dimensional vocabulary.  The mirrors are one of the main parts of the kaleidoscope, because it allows the objects’ images to reflect around them to create the typical symmetrical effect.  To me, this is extremely similar to Escher’s Circle Limit III, in which the objects repeat in a circle with equal angles separating the patterns.  What makes them different, however, is that Circle Limit III focuses more on space, while a kaleidoscope focuses more on motion.  According to Henderson’s article, “because of the time element in hyperspace philosophy, motion also became in important attribute of the fourth dimension.”  One of the main features of a kaleidoscope is to rotate the end of the tube to cause the small objects to move around, which creates new patterns while the entire image is rotating.  This creates an element of motion in a kaleidoscope.  When I was researching about Circle Limit III, I came across a website that creates a kaleidoscope out of Circle Limit III.  I thought it was interesting because it fused these two aspects together. 

http://agutie.homestead.com/Files/escher/escher_circle_limit_1.html

Also, according to the American painter, I. Rice Pereira, Einstein’s Relativity is defined as “a ‘pure scientific or geometric system of esthetics.’”  This is proof that a kaleidoscope is an example of mathematics with space and art because a kaleidoscope uses geometry to create the images in the shape of a circle, all with equal angles.

I found it extremely intriguing that Escher’s Circle Limit III and kaleidoscopes are related to each other, in which they rely on mathematics, geometry, space, and motion to create a fourth dimension.

http://www.d.umn.edu/~ddunham/dunham.am.pdf

 

Week 2 / Art’s Internal Logic / Stephany Howard

Monday, January 19th, 2009

In this class so far we’ve been conflating the terms art and design. As an artist I see a huge difference between art and design—they deal with aesthetics and function in very different ways—but our lumping them together for the purposes of class discussion doesn’t offend me. When I’m thinking about the role that mathematics plays in art and design however, I think we should make the distinction.
Math plays an obvious role in design—for an object to function in the physical world, it must cooperate with laws of nature. Designers must juggle with one hand their efforts to make beautiful things and, with the other hand, the very real physical constraints of materials and gravity. There are specific rules to making functional objects on planet Earth. Thus designers must deliberately acquaint themselves with the rules of the game—they must get cozy in mathematical fabric of our physical circumstances.
Artists however aren’t usually making functional objects. For this reason, an artist could easily get away with a less than refined appreciation for math and the physical laws governing our universe—hence Surrealism employed non-Euclidean geometry and the fourth dimension in their “militant” attack on logic…using math to attack math…
So an artist’s relationship to math takes curious forms and admittedly an artist’s mastery of math often proves embarrassingly superficial. Little do many of us know—or want to admit—how utterly determined our motions are—by math (the basis for the painters are stupid stereotype).
So designers use math in obvious ways, but what happens when an artist chooses to acknowledge math, to take interest in it, to address it in her work? Once she knows that the golden ratio may shape her aesthetic choices and her audience’s tastes for example, should she use that ratio to her benefit, should she reject it—should an artist employ math in a more than accidental way?
One could argue that while the sciences locate meaning, the arts construct meaning. When a painter sets out to construct meaning, she makes a series of choices: where to place the color on the canvas, next to which color, what shape, size, thickness, temperature should she make that mark—does she make it hot, cold, thin, thick, green, red, fast, slow, high or low? Ultimately she has to make these decisions, and for a reason. Where a designer makes decisions based on the logic imposed on her by an object and it’s desired function, a painter constructs a two dimensional reality with its own internal logic—as a painter, I want this logic to mean something.
When I paint in order to construct meaning, I want to have good reasons for every decision I make. Math sometimes gives me those reasons. I use math in order to emancipate my picture from the inevitably generic fate it arrives at through merely intuitive decision-making, to ground it in an order outside of my subjectivity, which is likely quite similar to that of other human beings. My experiences, expectations, intuitions, hopes, fears, assumptions are likely not all that different from yours so if I want to surprise you or move you in a new way—I have to employ logic that transcends this subjectivity. I use math to make novel images, to introduce chaos where my intuition might otherwise fight to control it.
Each of the artists linked on the webpage have different logical structures that they work within, they each have unique reasons for producing objects or experiences the way they do, and subsequently math plays a unique role for each artist. Musicians work within an obviously mathematical system because, as Tony Smith says “music has a mathematical structure.” (http://www.valdostamuseum.org/hamsmith/musPhys.html) Around 2500 years ago, Pythagoras discovered that:

(The Shape of Music, Dmitri Tymoczko http://seedmagazine.com/news/2008/07/the_shape_of_music.php)

For painters, the logic isn’t so obvious. Here, I’ll show you how math shapes my work:
When left to my own evolved creative devices, (link:http://www.seedmagazine.com/news/2009/01/painting_and_the_pleistocene_1.php)
I produce an image like…

(Here’s a scene that’s not all that unexpected)
Using some external logic, this image becomes…

Which eventually becomes…

In another example: With a system, something like…

Becomes….

Which eventually becomes…

I use math to discover places that I would never arrive at using intuition alone.
-Stephany Howard

week 2\ Math and Art \ Akhil Rangaraj

Monday, January 19th, 2009

I viewed math as an art even before taking this class. I have taken some art history classes before which have described the progression of the concept of mathematics in the arts, from the golden ratio to the science of perspectives. However, I didn’t realize the idea of the progression of spaces that happened after the initial discovery of perspective and ratios. Linda Henderson’s article was particularly enlightening with respect to the progression of art techniques and their relation to science. The paradigm shift induced in science by the theory of special and general relativity also reflected over into the world of art.

In lecture, we went over different mathematical ideas that are present in the arts, and indeed, nature itself. One of these is the concept of the golden ratio. The video on transforming a man into a woman using a simple template based off of ratios only underscored the ubiquity of mathematics. Furthermore, other examples, such as the behavior of stock markets fitting into a spiral was truly mind boggling. The lecture made mention of a Arabic scholar. Much of the architecture from the islamic world during this time period made use of geometric concepts and patterns (a style known as arabesque).

Looking over some of the links provided on the course website, my attention was immediately drawn to the description of the Mandelbrot set. Fractals were covered in class, but the description on the website included detailed mathematical information. I won’t pretend that I fully understood the details, but it was still impressive . The iterations the equations take through the complex planes seem to fit perfectly into the idea of a sort of fourth dimensional space. Not only this, but varying the parameters through the complex plane result in entirely different images. Finally, with regards to this article, all the mathematical mysteries behind this set of fractals have yet to be solved, which is quite amazing.

I searched the internet to find similar mathematical artworks similar to that of the mandlebrot set. I came across a website that used a different rendering method to generate a mandelbrot set that sort of resembles a seated Buddha.

This alternate rendering method contains the same mathematical elements as a standard Mandelbrot set, however the method in which they are presented are entirely different. I think this underscores the importance in how data is presented to us.

Buddhabrot: http://www.superliminal.com/fractals/bbrot/bbrot.htm

Animated: http://www.youtube.com/watch?v=nBXqnN7vNzk&feature=related

A “buddhabrot” being rotated and manipulated in 4-d space: http://www.youtube.com/watch?v=5ej3dj4×64k

Akhil Rangaraj

Week 2: Can math be beautiful? By: Claudia Zapien

Monday, January 19th, 2009

 When you think about math and art do you usually think of them in the same context? The truth is that when I used to think about art I would imagine something beautiful and creative and when I think about math I think about numbers, formulas, and most of all headaches. The truth is that math has a lot to do with art and art with math. The branch in math that can most easily be related with art would be geometry. Geometry is the branch of mathematics that analyses the shape, size, and position of a figure.  When it comes to art there really is not a guideline on how to draw, but it just so happens that most pieces of art that are pleasing to the eyes have some sort of mathematical basis. After the lecture on art and math I began to see things as a combination of art and math instead of keeping the two subjects separate.

I have always thought of the Louvre Pyramids to be a beautiful building. Of course in the back of my mind I always knew that the construction of that beautiful piece of art was possible due to the advances in math, science, and architecture, but I never saw the structure its self to be mathematical work of art. Now that I think about it, I find it to be pretty ridiculous that I never saw the connection between math and art because the building itself is a huge pyramid and the walls of the pyramid are adjacent diamonds. The entire structure is nothing more but a combination of shapes, angle and lines that come together in such a beautiful way that the building itself is a work of art. We are so conditioned to label everything, and we want everything to fit into a category that we stop looking at the whole picture and realize that everything is unique a combination of different branches coming together.  

 Other than the exterior of the building being inspired purely from math, I find it fascinating that one of the reasons why the entrance of the museum was in the form of a pyramid was mathematical.  A pyramid shape would offer maximum surface area of the building while minimizing the volume needed to build the structure. It was important that the building not occupy a lot of volume because if it did it would take away from the palace, also the maximum surface area was important because the building was supposed to have warmth to it that would be achieved by natural light coming into the building. Not only is math used in a very simple way to choose the best design for the entrance, but it is said that pyramids are very mathematical. When we analyze the structure of a pyramid we encounter the concept knows as Golden ratio and it is calculated by diving one of the lengths of the base of the pyramid by the height of the pyramid. The result is an astonishing ratio of about 1.6 and this number is found all throughout nature and art.  It seems that things that are aesthetically beautiful and pleasing to the eye fall under this category.       

I think that another factor that makes the building beautiful is that fact that it brings the old and the new together. The concept of pyramids as buildings is an old tradition used by various groups such as the Egyptians and the Mayan as important cultural buildings. Because the previous groups that used pyramids used them to symbolize a sacred location, this building also makes us feel that what the building its self and whatever it contains is something that should be appreciated.

-Claudia Zapien

Week 2

Monday, January 19th, 2009

Here is a picture of a terresact rotating around plane in 4D. Just looking at this picture, we can automatically tell that  a fourth dimension has required so much efforts to discover. When Leonardo reports that a Non-Euclidian geometry, also known to describe hyperbolic and elliptic geaomtry, never achieved never achieved the popularity of  the fourth dimension, I think he is totally right because shapes in fourth dimension are composed of extremely complicated geometry. He also reports that the enigmatic view of  shapes in fourth dimension caused many scientists not to want to pursue studies in a four dimension. This result is most likely to be authentic to humans. Generally speaking, in actual generations scientists do not  spend as much time as  old ones did. It is true that old scientists dealt with tough cases too. For instance, the U-V catasdtrophe. But in general, I think today’s scientists are less motivated or fascinated into subjects such as connecting the fourth dimension to the Non-Euclidean geometry. The fourth dimension named “time” after scientists applied differents theries to it became somehow one big  tool that connects artists and scientists. As I reported in my last blog, science and art have always been or worked together. One acts as a complement of the other.

 

 

As most of us can recall, what we have above are pictures of geometric figures that we are familiar with.  Hyperbolic, Euclidean and Ellipic  shapes that have been explained in science but made possible to visualize through art. Again art and science together equals world’s view in the fourth dimension. The reiterate in the discussion of time as a fourth number, I would like to interpret what is reaelly going on in this pictuure. We see the earth globe on a sort of  like a moving plane.  If we were to look down this picture is a, we would merely observe a 3-D which is refered to as the world we live in plus a one dimension plan known as time. In other words, the world moves as time goes by. I believe representing it in a such way is good because it gives a perfect view of  what it is to live in a moving planet. This is relevant to us or especially to me as an aspiring scientist in that it makes me estimate how much the world will change by as time the fourth dimension goes by. The beauty of  the insertion of art  in such a matter is to allow one to visualize what the subject is.  So science can be so complicated without pictures or pieces of art as illustrations.             

By Fabrice Keto

week 2 \ a different mathematical sort of art \ ben marafino

Sunday, January 18th, 2009

Let me begin by discussing a phenomenon that may seem wholly mysterious, even after explanation – but at the same time “artistic,” if only for its mystery and aesthetic appeal. Suppose we heat the bottom of a layer of water, for example, which is much wider than it is tall, and allow the water to lose this heat through the top layer via radiation (the two layers are perfectly flat panes of glass, say). Then, the temperature of the bottom layer is gradually increased until something quite curious happens – the water sorts itself into very neatly ordered ‘convective cells,’ or Bénard cells, as they have come to specifically be called. Within these cells, a small quantity of warm fluid rises until it encounters the cooler top layer, upon which some heat is lost; the cooled fluid then descends, is heated up again, and retraces its previous journey. It is much easier to observe this effect if small (e.g. aluminium or other metal) particles are also mixed with the water, as in the picture below. You may have even observed this sort of effect yourself taking place, for example, in a bowl of hot soup or coffee that has just been mixed with milk.

What, exactly, is so (perhaps aesthetically) interesting about this phenomenon? Consider that convection typically takes place on roughly the same size scales as the liquids being heated – for instance, if you heat a pot of water, you will most likely observe one large and disorganized convective cell, if at all. More likelier still is some sort of random, turbulent pattern of convection, but the uniformity of heating does plays a big role. However, if you were to considerably flatten that pot and then gradually (and uniformly!) heat it up from room temperature, this random convection will, as explained previously, mysteriously organise itself into a series of smaller cells with themselves even more curious properties. For one, no two adjacent cells (in a straight line) have the same direction of circulation when viewed from the side – one will rotate clockwise, the next counter-clockwise, the one after that clockwise, and so on. There is an intriguing mathematical explanation for this effect (as well as for the formation of the organised cells themselves), which unfortunately falls far beyond the scope of this blog post – let’s just say it has to do with something called ‘spontaneous symmetry breaking,’ - this year’s Nobel prize for physics was awarded for its discovery.

But what truly lies behind more complex processes – say, (the atmosphere [which really ought to be included]), life, the universe, and everything, and what has this got to do with art? ‘Minimization of entropy’ or another similarly emotionless term does not exactly evoke the same romance that the process of generation of art might in us - the human creation of art is arguably just as spontaneous as these simple physical processes may be, yet art has remained, and will remain, generally resistant to the instruments of reductionism. It is for this reason – and perhaps this reason alone - that we approach art, as we do with the world that surrounds us, with some measure of awe. However, our insights into such human pursuits, along with our quantitative treatment of complex physical systems (of which the behaviour of fluids is one), fail to provide complete descriptions of the underlying processes. We can say exactly (without resorting to silly pop-evolutionary psychology claptrap) as much about why the Mona Lisa was created as we can say about, for example, what the weather will be like two weeks from now: nothing definitive. Both cases manage to evade not only explanation, but our entire system – as it stands now - of coming up with them!

Week 2/Mathematics, Perspective, Time, Space/By Erum Farooque

Sunday, January 18th, 2009

I always thought artists had it so easy. All they do is paint pictures, or design some other visually appealing piece, sell them, and go out to fancy parties if they were successful. It seems like such a easy and fun job of only creating beauty, so much more so than anything south campus has to offer. I got even more of that impression from an art major who lives on my floor and never has homework and parties nonstop, always drunk as well. However, viewing all the artwork the T.A.s had done in their art careers so far made me realize that art takes a lot of dedication, patience, skill, and long hours only to end up with something, sometimes, that only makes sense to you. It ending up being too abstract with no meaning would be frustrating. I wanted to be a graphic designer because it sounds fun and not extremely difficult. Tweaking and creating images on the computer sounds nice for a profession but the pieces of art every T. A. created looks like it took a lot of time dealing with every little detail on the computer.

Art is very much based on perspective. People can see one piece as beautiful while another can declare it nothing but trash. Also, different people have different perspectives and see different ideas, pictures and things in the same work of art. Optical illusions work the same way. The two optical illusions that Professor Vesna showed in class are very common optical illusions that i have seen before so i found two other very common pictures that come out different based on your personal perspective.

http://www.optillusions.com/dp/1-9.htm

http://www.optillusions.com/dp/1-14.htm

Going through that website will give you more remarkably interesting pictures that change based on your perspective.

It was very interesting when Professor proved the requirement of math in art. I never knew art used so much math in it and really was amazed at how the best works of art use so much math. The golden ratio that is used in art  was hilarious when applied to the face. It was very interesting to see that the faces of the “beautiful people” matched the golden ratio face perfectly.

Reading the article “MUSIC and THE PHYSICAL UNIVERSE”, I realized how math can be applied to music as well as physical art. Math is applied to physical art by using ratios and proportions to measure the figures to resemble reality. Math is applied to the musical world as well, along with physics, through the construction of the musical instruments. Without math one could not properly build the instruments because you need math to be able to tell what size everything should be and how tight the strings should be to make the perfect desired sounds.

Week2: Perspective by Joon Jang

Sunday, January 18th, 2009

Perspective may be the most important out of all the aspects of art.  It also is very fast in terms or its evolution.  Julian Beever’s pavement paintings use anamorphosis, where the viewpoint must be precise in order to see it “the right way.”  The usual linear perspective isn’t discarded, but rather modified in order to create this illusion of three-dimensionality.

Time square in time square

Time square in time square

Anamorphosis isn’t only for paintings. Donatello’s St. Mark, for example, is “out of proportion” when viewed at the street level.  It is said that for this reason, the linen guild that hired Donatello rejected the piece.  However, Donatello promised to make adjustments, and without altering the work, placed the piece in the niche that it was to be placed (higher than eye level), then presented it again to the guild after 15 days.  Seeing it from the viewpoint that Donatello intended the viewers to see, the guild accepted the work.
In some ways, I believe, anamorphic art is more real to life than other arts in the sense that everything looks different in different perspectives.   People often have a “distorted” point of view in different ideas, but are they really distorted?  Anamorphic paintings appear distorted if not viewed in a certain angle, but how can we say that it is distorted if the painting itself hasn’t changed?  As for paintings with linear perspective, the perspective is given to the viewers and they have no freedom to explore the work in other ways, while anamorphic paintings, the viewers are free to look at it in different perspectives.  It is the human willingness to change their perspectives is what fuels the evolution of art.  Perspective in art is both dependent on the artist and the viewers (it is up to the viewers whether to see the art as art or not, for example).
Also, perspective was the gateway in art to add new dimensions to it.  No longer is art set within the boundaries of Euclidean geometry, due to the evolution of perspective.  Time and movement, which is one way to look at the fourth dimension, is now more prevalent in visual arts then before.  Of course, movement was always meaningful in art (such as in dancing, or the exploding shapes in fireworks), but now, moving pictures, or even moving sculptures are possible, adding more dimension to artwork than before.  What caught my attention when I was a child were the video art pieces by Nam June Paik.  I remember the multiple TV’s functioning as one screen to project the moving pictures.  Sometimes the TV’s were arranged to make different shapes, which made the pieces sculptures at the same time.  In viewing video art, the perspective isn’t limited only to the viewpoint, but also the viewing time; in order to see the whole “picture” one would need to stay and watch the whole clip; Paik successfully added a fourth dimension to his works.  http://www.paikstudios.com
Perspective is the essence of art.  Without it, how can we have the view points of what is art and what isn’t?

Joon Jang

Week 2\Volumes and Math\Amy Chen

Sunday, January 18th, 2009

            I thought it was really interesting this week to read about how artists of the past have tried to find and paint the 4th dimension in Henderson’s “Geometry in Modern Art.”  I enjoyed reading about the cubist artworks and how they’ve tried to depict all perspectives of an object.  I remember seeing a painting of Picasso’s at the Hammer Museum of a guitar.  It showed the strings, the back and front of the guitar, the texture of the guitar and even the black hole inside the guitar, which was depicted as a black rectangle.  In lecture we could tie this to the painting Professor Vesna showed of a figure descending the stairs.  It’s as someone had taken a picture of someone with a show shutter speed, you see the figure at the top all the way to the bottom; the areas where an arm might interlock with it’s previous location can be seen in more dense concentration of paint.  I thought the artist’s depiction of the 4th dimension were really interesting.  I also felt one of the TA’s works was related, he did a sculpture of a a falling leaf and captured the interlocking volumes together in a sculpture, this reminded me of Boccioni’s “Unique Form of Continuity in Space” (Shown Below).  Since in Section D we’re allowed a lot of freedom with our blogs, I also decided to do a similar idea.  I drew roughly 15-20 figures (with 90 seconds each), different perspectives and different poses, but began all figures at a general head area.   Not as cool as the sculptures though haha.

 

It’s cool to do a rendition of an idea based off of what others have done.  Looking at Boccioni’s sculpture now, it’s kind of easy to see where he got his form, as his and my rendition of continuous movement are slightly similar.  

 

And about Fractals, I didn’t realize just how much math is involved in fractals until I looked it up. Pretty crazy  (http://www.hiddendimension.com/Mathematics_Main.html)

This is another interesting link for art of the 4th dimension. (http://www.strangehorizons.com/2002/20020916/fourth_dimension.shtml)

 

Week2/Art, Science and Monkeys Part2/Connor Petty

Sunday, January 18th, 2009

Mathematics is universal. That is why it is easiest for an artist to use mathematics in order to express his or her creativity. Math defines fundamental shapes: triangles, squares, etc… that are instantly recognizable in anyone’s eye (unless they are blind). But using math to create art is not like painting a canvas; it is like looking through an infinitely large gallery and picking painting that you like. To me, that doesn’t seem like something that could very well be considered art.

borg cube

Take the above picture is an example of such a piece of “art”. As interesting as it looks, it is precisely defined by an equation. Because it is defined by an equation, it can viewed anytime and in any perspective with the help of 3d rendering software. The problem arises when I attempt to see the human element of the “artwork” because it really doesn’t exist. No human participated in the drawing of the image, because no human could draw it. It is what this class deems “mathematical artwork”. To me, “mathematical artwork” is not real artwork because real artwork is “human” artwork. If a person made a painting based upon the above image, I would deem that painting as artwork because a person actually drew it. I’m not saying that artwork cannot be produced with the help of tools, tools do not remove the human factor. Even if an artist uses a compass to draw a circle that doesn’t mean that the circle cannot be deemed artwork. As long as a person controls the production of the piece of work, it can always be considered artwork.

With that in mind, technology can be a very valuable tool to help an artist create his or her work. Take for example this video: Painting Mona Lisa with MS Paint. Even with the simplest computer painting tool, MS Paint, it is possible to create a famous piece of artwork in far less time that it would take otherwise. But always bare in mind that the less time it takes to create a piece of artwork, the less important that artwork becomes. If a piece of artwork can be created instantly, then it might as well have not even been created since the tools creating it are so extensive that dropping a rock on the keyboard to hit that “create” button would be more artistic than the image that appears on screen as a result. An artist should never rely on tools so much so that a trained monkey could create an identical piece of work in the same amount of time if given those same tools.

week 2/math and art/paige marton

Sunday, January 18th, 2009

In this weeks lecture, Mathematics, Perspective, Time and Space I learned about many awe-inspiring happenings in nature. To be honest I wasn’t looking forward to this lecture; just the word mathematics is intimidating to me. But I was pleasantly surprised. The affect nature’s formula has on modern day life and design that’s reflected in the golden ratio is astonishing. This chain of efficiency lead me to think about the way we treat our environment and how truly essential it is to our way of living. Buckminster Fuller always respected nature and acknowledged the limited resources the planet and nature has to offer. “A wondrous new anthology about the planet’s friendly genius. Read Bucky’s legacy about a greater understanding and appreciation of our world and the resources we are granted. Start the 21st Century off with a true visionary ahead of his time.” –Mark Elsis

          As I sifted through the many artist websites provided on the homepage one in particular stood out, Nathan Selikoff. His artist statement really moved me. His work links art and mathematics, which could be seen as polar opposites, but with society evolving, the two seem to be closer than ever. Technology is his medium and he creates beautiful artwork through his own interactive programming. My favorite pieces (which can be found here http://www.nathanselikoff.com/strangeattractors/) are a reflection on “the complexity of simple mathematical functions”. I would never imagine linking mathematical functions and art together, yet the results are breathtaking.             

            In lecture we looked further into the world of the golden ratio. I was very excited to focus on the ratio because the recent artwork I’ve produced at ucla is centered around the idea. With the discussion of the golden ratio came a number of related topics such as fractals and Fibonacci’s sequence. I never realized natures ability to create efficient growth could be translated into product design and economics, the video Fibonacci, fractals, and financial markets: socionomics was mind blowing. I loved learning about new ways the golden ratio affects everyday life. It really made me appreciate how extraordinary nature is.

            With Nathan Selikoff’s concepts in mind, I found a blog with a focus on technology, mathematics, and software in art and design. http://www.generatorx.no/ generator x focuses on art from code, which I do not practice, but I still found it very interesting.  Another interesting resource was generator x’s flickr account that showcases other mathematical artwork. http://flickr.com/groups/generatorx/ With all these sources in mind, it is quite obvious that art and math do have a natural connection. 

-paige marton

 

             

Week2/Fine Artist v.s. Photoshop/ Lam Tran

Sunday, January 18th, 2009

Ok, so my sister is an “artist.” She has a degree in motion graphics (design art) and a background in fine art. She told me that there is a split in the art field: Design art and Fine arts. This class, our T.A. ( atleast the stuff in their portfolio they showed on thursday) and our professor are into the Fine arts. This is often seen as the more abstract, but hardcore art.

O.k. now to go into the stuff we learned this week:

The vanishing point, 3d objects, shadows, mirror reflections etc. can all be automated by simple clicks in photoshop. Adobe photoshop is only one example, and the most well known one (that is why i chose to include that in my title), where careful calculations are no longer needed to make shadows and such realistic. Back in the 1900’s ,where this Non-Euclidian art was starting up, and technology primitive at our perspective, calculations and backgrounds in math were required to make their art more realistic. In terms of 3d objects, the geometric calculations were required to actually make sure the peices fit together. Nowadays, all these things can be simply done on a computer. If one wanted to make a 3d object, like Piero de la Francesca’s dodecahedron (from lecture), he or she can just type how big they want it on the computer and it will put out the angles   the pieces, the dimensions of each piece, and any other information required to make it. Going back to photoshop and taking vanishing point as an example, designer artists don’t have to worry about lighting or planar projections to make the vanishing point loook realistic. There is vanishing point tool that one can just use or you can do it yourself by manipulating the planes (like how Filippo Brunelleschi did in the 1415) but now much easier. Here is a comical tutorial of it:

http://www.youtube.com/watch?v=wH6-twlgJhU

N0w to relate this to my first paragraph:

Fine artists, like the instructors in our class, do not take the shortcuts that technology provides. They try to do something new and different. If they do use the “shortcuts” that computer programs offer, it is to enable them to do something even further in half the time. It, in a way, is “harder” or requires more work than just designers who only use programs, such as photoshop, for their work. Some of our TA’s work that they showed this week looked too abstract that I didn’t know or couldn’t really appreciate it but at least i can respect it because they spent all the time and effort, doing all the small things to put it together. This is in contrast to the design art that looks cool with all its flashy colors and motion graphics (think pixar or i-pod commercials) which most people can look at and appreciate it immediatley. What I am getting at is that even though I may not like the fine art being showed in class, I can at least respect it and all the hard work the artists put in to make it.

LAM TRAN

Week Two, math, Yu Hsiao

Sunday, January 18th, 2009

 

In the lecture, there were a lot of references of beauty being connected to the golden ratio, Fibonacci’s ratio, etc. It seems like beauty matters, a lot. In modern media, there is sort of this ideology that we shouldn’t be so shallow and always emphasize beauty. We should look for personalities rather than the looks. But the truth is, beauty does matter. In a research done by BBC, babies were exposed to pictures of individuals, some ugly, and some very pretty. The babies cried or stayed away from the ugly pictures. And of course, the babies spent more time around the beautiful face of a woman. Studies also show that beautiful people get better paid jobs, and get better opportunities in a society. So the question is, is this potent force in our lives, our connection to beauty, a total subjective thing where it is different from person to person, or is there, a very scientific, and universal rule to beauty?
It turns out that, scientists have found a pattern for beauty. One of them is the golden ratio. We can see the golden ratio celebrities’ faces, such as Angelina Jolie, or Elizabeth Hurley. The dimensions of their faces have direction connections to the golden ratios. Other works of art, such as the Parthenon, which is considered one of the most beautiful architectural works of the Greeks, have also connections to the golden ratio. So it’s definitely not a coincident that the golden ratio is apparent in beautiful things. Though we can say that if something has the golden ratio in them, it could be beautiful, it is my opinion that we can’t say a person and anything must have the golden ratio to be beautiful. Beauty is completely subjective. The picture of the ugly person in the youtube video I posted, might be found beautiful by other babies. With Popper’s view, mentioned in the last week, we cannot simply prove that all babies find that picture ugly, so therefore, we can assume that there must be some individuals out there who would find that picture attractive. I also talked about this with my friend. Each person has their own sense of tastes for the opposite sex. We came to a conclusion that everyone will find someone that will find them attractive. If not so, then how do couples, of not so good looking get married?  Individuals will all find beauty in things that have no golden ratios or other connections to scientifically proven patterns.

In the lecture we also talked about how beautiful music can be created through mathematical equations. One example was a website that had music that were made from mathematical symbols. There was a music made based on the pattern of pi. There was a piece of music made based on the patterns of the Pascal’s Triangle. It bothered me that, they made music from math, and feeling-less functions, instead of making music that expressed their feelings. I agree that, we could probably find, a universal pattern, like the golden ratio, among all good pieces of music. But I do not think music should be created from solely from mathematical equations. Music should be created from an individual’s creativity and feelings. It’s meant to be performed by a person to express one’s virtuosity in music, and also one’s feelings. To make sounds based on mathematical origins, then it destroys the whole purpose of music.

I have been in a band for 3 years now, and we’ve performed at some concerts in our high school. To me, music was about performing in front of an audience. No matter how big or small the audience is, I feel that playing music is connecting with my audience. It could be a crowd of three hundred people, or it could as small as a single loyal friend. Playing music made from feelings, and creativity of one’s own unique mind expresses words of meaningful stories, that comes from one’s experiences, encounters, and journeys. I feel that the music presented in the lecture this week has almost no meaning. Though it might sound nice, and delightful, or beautiful in some people’s perspective, after all, the music itself is made from a bunch of numbers. Surely you can argue that those numbers come from nature, but there’s no stories behind those numbers that we can relate to as individuals. In my second youtube video, this is a concert held by the famous band Queen in the Wembley Stadium. We can see that the singer makes connection with the audience, and the audience sings with the singer, making the vibe of the song constructively unite together. It makes the music more meaningful, when you can connect and relate to the story behind it.

I think this week, the professor is trying to teach the idea that beauty and science can be fused together, and beauty can be scientifically engineered, such as the perspective drawing, where if the artist makes correct mathematical measurements, then the drawing can be near perfect and have beauty. I agree that those scientific patterns could be found in works of art that contains beauty, but I do not think that works of beauty should created from those patterns. Rather they should be created from emotional creativity. Also, how we judge beauty in people in general should be also how we feel, rather than sticking by those scientific ratios. If we make things based on those guide lines and ratios to make them beautiful, then we might as well be robots that make things based on what we know, rather than what we could make out of nothing, by imagination. After all, according to Einstein, imagination is more important than knowledge.

http://www.youtube.com/watch?v=1AZe9g2Huz0
http://www.youtube.com/watch?v=u8-rH2ilkxk

 

Week 2\Math with Art\Jay Park

Sunday, January 18th, 2009

http://www.graphica.com/gallery/trott9.html

In my eyes, the art has to make sense. The inevitable requirement of great art is therefore the necessity of the art in question to obtain a sense of beauty from what my mind is geared towards–math. The art I appreciate, like the math I know, flows constantly and smoothly without jagged edges and blunt finishes. The flow of the equation is effortless and balanced, as it tells a tale of a thousand words in one snapshot. As math can show acceleration, velocity, and distance travelled all in one static page, so too can the unique efforts of artistic minds show the movement of a nude down a staircase on canvas. When looking at an image, the inherent limitation of stillness in such a medium engages the artistic creativity to show that which isn’t possible. The sense of progressive time erupts from the stillshot perspective through ultimately the use of mathematics. The transposition of repetitive imagery produces a linear progression of time and dynamics that others argue starts from art to math, not the other way around. I cannot deny this claim, but nor can I claim it as true, since in my mind I find the math necessary to understand and create the art. In other words, there is subjectivity in assuming art the predecessor of math, or vice versa. 

 

http://darkdestroyer.wordpress.com/2007/09/12/2009-nissan-skyline-gt-r/

The engineering feat of the new Nissan Skyline GT-R exemplifies the beauty that results unintentionally from perfected mathematical model. All the crevices, crooks, angles, and edges are engineered, designed, and crafted to fit one driving purpose–to channel all the windforce to the huge spoiler in the back for the necessary downforce to the rear tires. Consider the concept drawings  in the video. Was the mockup design drawn before any mathematical consideration was given? If only we knew the progression of the design team. It is safe for me to speculate, however, that the mathematical consideration came before the beauty. I justify this by asserting the historical background of the Nissan Legend’s race-performance pedigree. Beyond style comes the absolute goal of performance worthy of the Skyline lineage. From this dedication to performance, came the design that would accomodate the traditional front engine, rear-wheel drive setup–the front-heavy posture, the thick and wide-spread rear stance. The necessity of a dynamic weight adjustment to the rearsets for variable highspeed traction turned to aerodynamics for help. The result is a sleek, aerodynamically slippery design that looks just as good as it performs. 

Both sides of the case can be made between art then math versus math then art. Therefore, I can only assert that it is up to a subjective, individual assessment as to determining which came first and which was more important. Nevertheless, it is obvious that math and art share a common result. Mathematical optimization and artistic perfection often go hand in hand and this understanding is one of the most amazing things about the natural world we live in.

Week 2/ Mathematics in Art / Andrew Curnow

Sunday, January 18th, 2009

Through out the seemingly separate realms of ‘Art’ and ‘Mathematics’, major differences are easily apparent. Even a first grader can distinguish a mathematical problem from a mundane finger painting. In essence, to the naked or untrained eye, Art and Math are undeniably different topics. However, even in my own inexperienced mind, mathematics can form an art of its own. Granted a sketch or a doodle may be completely derived from the simple mind of a toddler, if applied correctly, mathematical principles such as the Golden Ratio, fractals, and even exponential growth in nature can give ‘art’ a new name. In fact, in the minds of many mathematicians, the numbers and problems form an art form of their own. As G.H. Hardy once said, “There is no permanent place in the world for ugly mathematics”.

            Of course, imposing mathematics efficiently into art is a skill of its own. Creating a masterpiece work of art or solving a math problem that takes 4 pages of calculations are each feats on their own, but to demonstrate a mathematical rule in a physical form other than numbers involves not only a proficient mind, but an understanding of the piece as well. For instance, if I glanced upon a work of art that was derived from the Golden Ratio as we observed in class, I would have no idea of the mathematical skeleton comprising the piece. When I realized the principles behind the various works of art we observed, the work itself changed in my mind, everything seemed to have a reason to have been designed the way it was. Another art project I researched and was very intrigued with was the project involving hypercones. At Basic Research Institute in the Mathematical Sciences at the HP Bristol campus, artist Simon Thomas has been researching and working with the idea of the Hypercone, in which a circle with an exponentially decreasing radius is modeled rotating through space.

The hypercone demonstrates the growth and decay that has always been present in nature. Furthermore at BRIMS (Basic Research Institute in the Mathematical Sciences) Simon Thomas works on pieces modeled from R. Buckminster Fuller’s geodesic domes. His variations follow the principles of Fullers domes in following the ruling that the needed strength of the building pieces must only increase in par to the logarithm of the size of the building. These both represent highpoints in the possibilities of modern day and futuristic architecture, found in the simple idea of mixing aesthetically pleasing artwork, which math.

http://plus.maths.org/issue8/features/art/

            These works demonstrate the innate properties that mathematics can take in art. Throughout history mathematics can be found fundamentally in works of art, whether in Escher’s or Buckminster Fuller’s work, or in works in which the pieces had extraordinaire mathematical support in order to exist such as ancient statues in which the hanging marble could not outweigh the suspension power of the marble or material. In essence, both art and mathematics can coexist easily, however it takes a correct mindset to truly grasp what is being introduced visually. Though I cannot say I am an artistic individual I can undeniably agree that the use of math in artistic forms is extremely intriguing. It demonstrates that such principles that most people claim “you’ll never see this in real life” can easily be visualized and demonstrated.