Posts Tagged ‘fractal’

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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