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.
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This is a very simple fractal. Fractals like the ones pictured below can only be produced with a computer.
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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.
Sikander uses his shapes to make us look at his art in different ways. In Sikander’s “Ways of Looking” we can see that he uses organic and geometric shapes in harmony to bring his picture to life. In the picture he uses geometric shapes to grab your attention as he uses the organic shapes to make us look deeper into the picture. The shaded circles behave in a way that make us target them and give them our first attention and then we begin to notice all of the elements around it.
While the studies at Governor’s School are noticeably more advanced and require more effort than at regular public schools, I see this rigor as the key to my academic success. For me, the classes I take that constantly introduce new thoughts that test my capability to “think outside the box”, are the ones that capture all my attention and interest. For example, while working with the Sierpinski Triangle at the Johns Hopkins Center for Talented Youth geometry camp, I was struck with a strong determination to figure out the secret to the pattern. According to the Oxford Dictionary, the Sierpinski Triangle is “a fractal based on a triangle with four equal triangles inscribed in it. The central triangle is removed and each of the other three treated as the original was, and so on, creating an infinite regression in a finite space.” By constructing a table with the number black and white triangles in each figure, I realized that it was easier to see the relations between the numbers. At Governor’s School, I expect to be provided with stimulating concepts in order to challenge my exceptional thinking.
Fischl creates a scene of chaos in this picture through the way he uses his paintbrush in the painting of the dress. The brushstrokes show in an untidy way, which creates a feeling that this woman’s life may be in chaos. At least, it has not gone the way she intended it to. Fischl expresses this through the sense that his brushstrokes do not seem to have gone in the way he intended them to. At the lower left part of the dress, it appears as though he could not be bothered to straighten the lines out or fix the colors. This seems to suggest that the woman, tired and disillusioned wit life, can no longer straighten it out, either. Her posture seems to follow Fischl’s painting technique and suggests hopelessness, as though she has tried everyone and nothing has made her happy.
Arthur Miller’s play, The Crucible displays the absolute control that the ego can have on not only the individual but on a society as well. A person may think that witch hunts are a confection of the past because as a modern society we do not fall victim so easily to ploys such as those which were created by the young girls of Salem. This however is untrue because within my short lifetime I have seen that we have been programmed to be fearful of terrorists, Ebola, and even ourselves. A great majority of these anxieties have been trumpeted by our media, elected officials, and religious institutions. In seeking my full liberation from such fears, I have come to the greater understanding that love and wisdom are the essential tools for setting one’s own courses. Hence, my purpose is to love unconditionally while sharing my own wisdom with those who have the shared interest; this is my path to liberation. Utilizing events which happened in The Crucible and connecting them to our current culture, I will contend that we still live in a state of fear and are still struggling to progress beyond that level.
Oprah Gail Winfrey was born on January 29, 1954 on a farm in Kosciusko, Mississippi to Vernita Lee and Vernon Winfrey. Her parents originally planned to name her Orpah, but the midwife made a mistake on the birth certificate.
"Oprah Winfrey Biography." -- Academy of Achievement. Ed. Hugh Esten. The Catharine B. Reynolds Foundation, 13 Nov. 2013. Web. 04 May 2014.
In the painting Castle and Sun, Klee was able to use three samples of geometric shapes to create his entire metropolis and applied excess space to design a skyline for his sun. Even though the shapes used consisted of miscellaneous versions of triangles and squares/rectangles to create the “castle” that stands beneath a wildly contrasted sun which stands as a focal point by being the only circle in the entire painting. In reference to the sun, the principle of proportion was used by the existence of a single circle larger than any other single shape within the painting that draws your attention to it which further supports the emphasis of the object.
On first thought, mathematics and art seem to be totally opposite fields of study with absolutely no connections. However, after careful consideration, the great degree of relation between these two subjects is amazing. Mathematics is the central ingredient in many artworks. Through the exploration of many artists and their works, common mathematical themes can be discovered. For instance, the art of tessellations, or tilings, relies on geometry. M.C. Escher used his knowledge of geometry, and mathematics in general, to create his tessellations, some of his most well admired works.
Named after the Polish mathematician, Waclaw Sierpinski, the Sierpinski Triangle has been the topic of much study since Sierpinski first discovered it in the early twentieth century. Although it appears simple, the Sierpinski Triangle is actually a complex and intriguing fractal. Fractals have been studied since 1905, when the Mandelbrot Set was discovered, and since then have been used in many ways. One important aspect of fractals is their self-similarity, the idea that if you zoom in on any patch of the fractal, you will see an image that is similar to the original. Because of this, fractals are infinitely detailed and have many interesting properties. Fractals also have a practical use: they can be used to measure the length of coastlines. Because fractals are broken into infinitely small, similar pieces, they prove useful when measuring the length of irregularly shaped objects. Fractals also make beautiful art.
Introduction: Have you ever wondered how Oprah Winfrey's life begun? If you read my paper, It will tell you everything about her life. Though she had bad experiences in her childhood she became the first richest African American billionaire. Her life started here. She was born on January 29th 1954 in Kosciusko North of Jackson, Mississippi.
It is constructed by taking an equilateral triangle, and after many iterations of adding smaller triangles to increasingly smaller sizes, resulting in a "snowflake" pattern, sometimes called the von Koch snowflake. The theoretical result of multiple iterations is the creation of a finite area with an infinite perimeter, meaning the dimension is incomprehensible. Fractals, before that word was coined, were simply considered above mathematical understanding, until experiments were done in the 1970's by Benoit Mandelbrot, the "father of fractal geometry". Mandelbrot developed a method that treated fractals as a part of standard Euclidean geometry, with the dimension of a fractal being an exponent. Fractals pack an infinity into "a grain of sand".
The issue of surveillance in general is a common one in society, but one specific facet of this overall issue is
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