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 over again found a way to harness the abstractedness of mathematics and coalesce it into their work. So where does this new art form of fractal design stem from? The naive realism is that fractals themselves atomic number 18 relatively young in the mathematical world. Of course since the let outgrowth of art and history and mathematics, self-similar objects have existed and been intriguing to the human mind. However it has except been recently that mathematicians have begun to explain them. So the question is posed, what is a fractal? Fractals are actually very bare(a). A fractal is any design that contains self-similar images within itself. ace real-life example would be a circulatory system. Each single argument vessel resembles the overall shape of the system. 2 The ma in characteristic of the fractal is its self-similarity. That means that individually part that makes up the unharmed resembles the whole. A fractal is then generated from millions of smaller images that unneurotic form a larger similar image. Nowadays, most fractals are through with(p) with the computer. This is because it is very slow and tedious to do the work by hand. However, slightly simple fractals such as a Koch curve or a Sierpinsky trilateral 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 gradation would be repeated over and over until a snowflake forms. The outgrowth of repeating the process five times is shown below.3This is a very simple fractal. Fractals like the sensations pictured below can only be produced with a computer.1Notice the self-similarity in the pictur e. 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.