Tuesday, October 26, 2010

Week 1 : Let’s impress people with Fractals 

Koch snowflake

Fractal geometry is a new branch in mathematics. Usually, mathematicians try to resolve problems such as calculation of volumes, surfaces of mountains, forests, lung surface, blood vessels with Euclid geometry. This was before Benoit Mandelbrot, a Franco-American mathematician tried to find a way to make geometry resemble what is found in nature and more precisely what geometry deals with : the shapes. As he said "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." In other words his will was to find a way to better a mathematic approach of natural diversity. The reason that made him think mathematics could help was the fact he noticed  that the concept of self similarity was applied. One of the most stunning example to understand this concept would be the look of a broccoli.

Each part of this Romanesco broccoli looks like the broccoli itself, and the subdivisions of these parts also look like the parts and so on.

During the first world war, a French mathematician called Julia tried to find out what would happen if a function is applied over a number, then to the result of this function and so on. The reason why he never found out was the lack of a computing tool in order to calculate the infinity of  numbers of this mathematical set.
Based on this research, Mandelbrot, who worked then in IBM performed this calculation on a computer and from this process the “Mandelbrot set” was born !

Mandelbrot set:
Emblem of fractal geometry

This is a famous picture and many people know what it is called but rarely know what it corresponds to.
This picture represents today the great finding of Mandelbrot . Fractal geometry has nowadays its application in many fields, many different technologies and also in art. It allows a more accurate way of perceiving natural shapes and phenomenon with mathematics and is a major step towards a science approaching as much as possible the nature of things as they really are.

If you are interested in fractal geometry and if you want more information here is a very interesting video describing how it has been a precious tool for cell phone technology, special effects, cardiology, imaging thechniques, art and others :

Bibliography/Webography :

Documentary movie "Hunting the hidden dimension" by Michael Schwarz and Bill Jersey

1 comment:

  1. This is illuminating stuff, guys. Thank you for these explanations on fractals, and thank you for the link to the video which was also quite enlightening. I cannot but notice as well the many similarities between different fields of study like mathematics, art, but also literature (and more specifically a sub-field of literature called critical theory). As a matter of fact, the notions of iteration and self-similarity are quite familiar to critical theorists, though they don't use these terms in their analytical works. The first name that comes to mind is Jacques Derrida, a theorist of difference, who has defined the notion of iterability (he could certainly have used the term iteration instead) or citationality to point out the fact that every piece of writing is in fact only a repetition of previous ideas. According to Derrida (and to sum up), every literary work is nothing else but the echo or the reminiscence of previous works, and no writing is original...which is a notion that has made quite a few literary specialists cringe. This notion of iteration is also quite familiar to the field of gender theory, and more specifically in the context of conversations about performative behaviors. If you ever encounter the work of Judith Butler, you'll learn that a certain number of thinkers have put forth the idea that our gender is constructed (we are not born men or women, we become men and women). The construction relies on the endless repetition of acts, traditions or other ceremonies, and regulative discourses that participate in inscribing individuals into a specific gender. So here again, we have the idea of endless iteration in order to shape our identity, our subjectivity, so that it fits into the normative cultural patterns we are supposed to adopt (this is not necessarily a conscious process)...
    In the end, this all leads to the conclusion that there are clearly many similarities between areas of knowledge (like mathematics and literature) which are, unfortunately, often thought to be quite unrelated...
    Thanks for your work!