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.
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.
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.
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.
Math is the study of fact that is based on experiments, proof, and facts, but there are many fallacies that go along with it, including the ability to neglect theories. As Einstein once said “that all our math is measured against reality, is primitive and childlike - and yet the most precious thing we have” Which shows that it might have flaws but it is still so brilliant and hard to defeat. In many aspects of human behavior, the arts, ethics, religion, and emotion, are some factors that can be slightly tied into the idea of math (Einstein Exhibit). The main problem is that it might be looked down upon because it might be considered illogical. Many people believe that there are no links between these subjects and math and that they are completely opposites, unrelated in anyway. If you look hard enough there are links between math and the arts, and can be found, even if math is not open to theories.
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.
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.
After being ruled by a prime minister for so long, France needed some changes. That is exactly what Louis the XIV would bring to France. In an age of separation, Louis wanted to start a unification process. He started this by giving himself sole power and also only having one religion for the country. The king is always the center of attention good or bad. Louis was prepared to take the good with the bad, and handled it well. He emphasized the king as the center of attention. While some see him as egotistical and greedy, Louis was one king who knew how to make improvements.
At the first glance, you see swirling lines that intertwine with vibrant blues, yellows and greens. The dark blue and black hues contrast the bright white and yellow. These lines appear to be thick brush strokes that create unity, and almost a texture feeling. Vincent’s painting seems to be looking over a valley town on a bright star filled night. The town is peacefully suggested next to the whirling clouds and stars. He suggests some kind of tree close up, and then layers the town behind it. The steeple is larger than the buildings and may represent unity within the town. The moon and stars are outlined like fireballs in the sky. The stars are relatively larger than the houses of the town. It leads me to believe
The issue of surveillance in general is a common one in society, but one specific facet of this overall issue is
Pointillism clearly influenced this painting, even though, unlike Seurat, Klimt never expressed an interest in utilizing optics in his work. Nine-tenths of this piece is a solid mass of foliage, thus if not for the tree trunks and strips of grass at the bottom, this composition would be completely abstract. The naturalistic elements of this piece are offset by Klimt’s decorative mosaic of green, blue and yellow dots, which are rendered representational only with the aid of the piece’s lower
Fractal Geometry The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things. The importance of fractal geometry is that it provides an answer, a comprehension, to nature, the world, and the universe.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.