Posts Tagged ‘mathematics’

Week 2_Maths, Art, and Biological Data Visualization_Wenjing Wu

Monday, January 19th, 2009

Most people tend to take it for granted that the form of art is wild and free with pure imagine. However on Tuesday Prof. Vesna talked about the artful beauty expressed by mathematics, a discipline which is usually linked to a bunch of formulas and rules. The part of perspective grasped my attention immediately, since that was also the topic of my drawing lessons this week. Our assignment was to draw a picture with four different perspectives. From Duccio and Giotto’s first attempt of introducing perspective into art, to Duerer and Vemeer’s  masterpieces that followed strictly to the mathematical rule, to the modern art styles like Cubism, which totally heads the opposite way of perspective, and then the way of teaching perspective in today’s drawing classes, artists are employing maths as useful tools and sometimes frames to break in order to creat “hacking” effects. I found a website discussing similar issues on maths and arts in National University of Singapore(poke me).

Do you see the strange object on the floor? Close your left eye, put your face close to the computer screen near the right side of the picture. You will then see a skull!

Do you see the strange object on the floor? Close your left eye, put your face close to the computer screen near the right side of the picture. You will then see a skull!

Artists use geometrics to fool our eyes, too. The famous painting above would be a perfect illustration. Besides that, there are also some artists using  Anamorphosis to produce astonishing 3D illusions, like Julian Beever.

On Thursday, our TAs talked about good jobs done by several students and also introduced briefly what they were working on. What I found the most intriguing is the part of John and Gautam’s–Biological Data Visualization. The works are simply COOL! As a senior student major in biotechnology, I know how overwhelming the biological data could become if it’s not well-organized–for example, our genome is consists of 80,000~10,000 genes, which roughly equal to 3000,000,000 base pairs. Moreover, since there’are needs to study biological process on different scales, organization and visualization turn out to be extremely urgent for biologists.  Some of the works appear to be very interesting, such as a project from the University of Tokyo(figure 2) and the research of Institute for Systems Biology (ISB).

Figure 1. High-Precision Three-Demensional Bio-Structure Modeling

This project enables the observer to track the distributions of different ingredients of foods through Internal Structure Microscope. Here, scientists is utilizing artful presentations to reveal its secret. As for the artists who are interested in latest scientific or philosophical ideas, as Henderson concludes in “Geometry in Modern Art”, are motivated by a desire to complete their subjective experience by inventing new aesthetic and conceptual capabilities. I suppose this might be a better answer for Gauvain.

Week 2: Math, The Bridge Between Art and Science by Ryan Andre Magsino

Sunday, January 18th, 2009

Week 2: Math, The Bridge Between Art and Science by Ryan Andre Magsino

Math, seperate from the sciences?

Math, seperate from the sciences?

Mathematics (or simply Math) is “the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically.” Although the definition sums it up quite eloquently, it does not specifically convey its relation to the sciences or arts. As we have explored throughout the week, there are several mathematical applications to both fields. As early as the 15th century, math has been utilized in order to explain perception and space. Artists have built on this application to determine vanishing points and formulate other artistic techniques. Science, on the other hand, is all about quantity, structure and changes. From the amount of blood pumping through the human body to the assembly of elements in a molecule, mathematics has played a somewhat integral part in determining those values. What then is math, a science or an art? American mathematician Benjamin Pierce refers it to “the science that draws necessary conclusions.” Yet another mathematician, Godfrey Harold Hardy, is “interested in mathematics only as a creative art.” Though it may seem one-sided at times, mathematical applications such fractals tie in both fields making it somewhat of a bridge between the fields.

Before looking into its applications, it is essential to determine what a fractal actually is and how it works. According to famed French mathematician Benoît B. Mandelbrot who coined the term, a fractal is “a rough or fragmented geometric shape that can be subdivided into parts, each of which is (at least approximately) a reduced-size copy of the whole,” however they can simply be defined as an image that could be infinitely found within itself. Fractals are often characterizes as having fine structures at arbitrarily small scales as well as being self-similar. A prime example of simple fractal would be the Koch Snowflake created by the Swedish mathematician Helge von Koch. It is created by first beginning with a single equilateral triangle then dividing all the sides into thirds thereafter. Last is replacing the center with a proportionate equilateral triangle. This process then continues onward for an infinite number of times.

Iterations of a Koch Snowflake

Iterations of a Koch Snowflake

Though we may be unaware, fractals have played a much larger and longer role in society than we have expected. Although it was only recently coined in the past century, American cyberneticist and ethno-mathematician Ron Eglash explores the implications fractals have left in African culture and society. ( Video - Ron Eglash: African fractals, in buildings and braids) Surprisingly, some African societies are structured in fractal iterations with multiple recursions. Looking now at modern technologies, fractals have also played a revolutionary role. It is due to fractal imaging we have such technologies as computer and video game imaging, especially when it comes to 3-dimensional modeling, and even fractal compression for image formats.

The first three iterations of the Square-flake

The first three iterations of the Square-flake

As for myself, I like to consider myself a mathematician (though nowhere as close as even amateur). Surprisingly, I along a few classmates in the past have developed a fractal we branded the “Square-flake.” Similar to the Koch Snowflake, the Square-flake is a fractal created by first beginning with a single square. In future iterations, the sides are cut into thirds with a square a third of the length on all sides is added to the given side. This process then continues onward for an infinite number of times. Taking it to a step beyond, we decided to integrate our fractal sequence and design. Our result was a fractal lamp. Taking the fractal to its third iteration, we were able to apply the concept into a work of art per say. (PDF: Square-flake Informational Pamphlet)

A photo of the fractal lamp unlit.

A photo of my fractal lamp unlit.

A photo of the fractal lamp lit up.

A photo of my fractal lamp lit up.

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