Fractals: A New-Age Mathematics to Explain Our World :: Fractals Mathematics Math Papers

Fractals: A New-Age Mathematics to Explain Our World Fractal art is a new-age art that tantalizes the eyes and mind with patterns, shapes, colors, and abstract imagery. Artists have once again found a way to harness the abstractedness of mathematics and integrate it into their work. So where does this new art form of fractal design stem from? The reality is that fractals themselves are relatively young in the mathematical world. Of course since the beginning of art and history and mathematics, self-similar objects have existed and been intriguing to the human mind. However it has only been recently that mathematicians have begun to explain them. So the question is posed, what is a fractal? Fractals are actually very simple. A fractal is any design that contains self-similar images within itself. One real-life example would be a circulatory system. Each single blood vessel resembles the overall shape of the system. [2] The main characteristic of the fractal is its self-similarity. That means that each part that makes up the whole resembles the whole. A fractal is then generated from millions of smaller images that together form a larger similar image. Nowadays, most fractals are done with the computer. This is because it is very slow and tedious to do the work by hand. However, some simple fractals such as a Koch curve or a Sierpinsky triangle can be created by hand. The Koch curve for example starts out as a straight line. Then, in the middle of the line, an equilateral triangle is formed. From that point, every straight line becomes split by an equilateral triangle. This step would be repeated over and over until a snowflake forms. The result of repeating the process five times is shown below. [3] This is a very simple fractal. Fractals like the ones pictured below can only be produced with a computer. [1] Notice the self-similarity in the picture. See how the smaller objects relate and mimic the whole picture. That is the essence of fractal art and fractal geometry. Similar to any branch of math or science, new concepts do not simply generate all of a sudden. Fractal ideas can be traced back to the late nineteenth century, however if one looks past that, they will see that the anchient Greek mathematicians also dabbled in the world of fractals.