The Art of Chaos
Abstract: In this paper, I will attempt to explain the nature of Fractals. Both natural and computer generated fractals will be explained. At the end, I hope the reader has a rudimentary sense of fractals in terms of both art and geometry.
Most people live in a state of semi-chaos. Isn't your cluttered desk an example of the chaos in the world? The words chaos and pattern seem to be a dichotomy, but fractals are both of these things. Basic definitions of fractals include the words self-similar, chaotic, and infinitely complex. Before I go on, let me first define the previous terms in order that the reader will understand their meanings as I will use them.
Self-similarity is the idea of an object where there is an apparent pattern in some visual or non-visual way. Sometimes, self-similarity is found with the naked eye, and other times a pattern appears under a microscope, or even when a significant change occurs. The major presumption of self-similarity is some type of pattern.
Chaos has been defined many ways through literature, philosophy, or even daily life. As I stated before, chaos is often used to describe disorder. The way I would like to use it is in terms of a certain unpredictability. Random events or iterations of the same even should cause a chaotic effect. Later, I will show how this is not the case. The last term we need to define is infinitely complex. As the term itself implies, fractals are things that go on forever. Why this is will be discussed later, as well.
In an ideal world, all types of fractals are self-similar, chaotic, and infinitely complex, but in the real world most natural objects are self-similar and chaotic, but not infinitely complex. Some examples of things that are self-similar and chaotic, but not infinitely complex are fern leaves, bronchial tubes, snowflakes, blood vessels, and clouds. Only one example in the world satisfies the three characteristics of a fractal, a coastline.
Coastlines are unique, because the length of a coastline is infinite, but the area within the coastline in finite. The theory of the interaction between infinity and finality is described by a fractal called the Koch Curve. Like coastlines, the length of the shape is infinite, but the area inside of it is finite. The shape of the Koch Curve is a triangle where a triangle one third of the size of the original triangle is placed on the middle of each side of the triangle.
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.
The fight for racial equality is one of the most prominent issues Americans have faced throughout history and even today; as the idea that enslaving individuals is unethical emerged, many great and innovative authors began writing about the issues that enslaved people had to face. Olaudah Equiano was no exception. In his work The Interesting Narrative of the Life of Olaudah Equiano, he attempts to persuade his readers that the American way of slavery is brutal, inhumane, and unscrupulous. Equiano manages to do this by minimizing the apparent differences between himself and his primarily white audience, mentioning the cruelties that he and many other slaves had to face, and the advantages of treating your slaves correctly.
“Chaos theory proves that unpredictability is built into our daily lives.”(Crichton 313). Ian Malcolm’s words resolve the book, Jurassic Park, in a very absolute way. Throughout the book, Malcolm, spoke about chaos theory and his self proclaimed “Malcolm Effect” to explain his reasoning in his predictions. Ian Malcolm had predicted the demise of Jurassic Park even before its opening, as well as its multiple problems and difficulties. Malcolm’s theory is evidenced countless times throughout the story of Jurassic Park; dinosaurs are breeding, dinosaurs are escaping, and systems fail.
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.
Equiano begins his autobiography with his experiences of slavery at a young age in his village and on the middle passage. For example, in chapter 1 Equiano reveals that his village also had slaves, who became as such by being a prisoner of war, as a punishment for adultery, or being kidnapped. There was no systematic slavery and the slaves from this village were treated as human beings rather than as property. Equiano claims their treatment of slaves was not nearly as terrible compared to the slavery of the New World. Based on this insight, Africans were not new to the idea of slavery, but were shocked at how horribly different they were treated. Despite this insight, there is a limitation because Equiano wrote his autobiography as an older man, meaning that his childhood memories were not easily recollected. In addition, in chapter 2 Equiano was kidnapped and made his way to the coast and aboard a slave ship. Equiano felt astonished and scared in the new situation he was in with the strange men. Below the decks, he saw the dejection and sorrow on the faces of other slaves. However, the slaves tried their best ...
"The Life of Olaudah Equiano” is a captivating story in which Equiano, the author, reflects on his life from becoming a slave to a freeman during the 19th century. Through his experiences and writing, Equiano paints a vivid picture of the atrocities and cruelties of European slavery. Ultimately through his narrative, Equiano intends to persuade his audience, the British government, to abolish the Atlantic slave trade as well as alert them of the harsh treatment of slaves. He successfully accomplishes his goal by subtly making arguments through the use of character, action, and setting.
The quest for power is one which has been etched into the minds of men throughout history. However, it can be said that true power is not a result of one’s actions but comes from the following one’s own beliefs without being influenced by others. This principle sets up the story for Shooting an Elephant by George Orwell. The protagonist, Orwell himself, is a sub divisional police officer in Burma, a British colony. Orwell must try to find and use his inner power when he is faced with the decision of whether or not to kill an elephant which has ravaged the Burman’s homes. The state of power established through the imperialistic backdrop show that Orwell, as a colonist, should be in control. As well, the perspective and ideas given by Orwell show his true character and lessen the overall power set up for him. Lastly, the symbols shown are representations of traditional forms of power, but take on different implications in the story. In Shooting an Elephant, George Orwell uses setting, characterization and symbols to show that true power comes from following the dictates of one’s conscience.
Randomization, in the form of mutations, provides genetic variation. Evolution itself is not entirely a random process, but the mutations that have appeared throughout history are. Because of this, one would argue that with the summation of many mutations over time, evolution would inevitably create more randomization within the system resulting in an increase in disorder. In an isolated system, the overall entropy would undoubtedly increase following a series of mutations. Because of natural selection (the idea that an organism that is better suited to its environment will survive and produce more offspring than those organisms who are not), it can be said that chance mutations are not the only driving force behind evolution, thus evolution is not entirely a spontaneous process (Williams,
Abrams, M. H. et al. The Norton Anthology of English Literature. Vol. 1. Sixth Edition. New York: W.W. Norton, & Co. 1993. 200-254.
Equiano has a firsthand account on the effects of slavery and the necessity of freedom. While describing a childhood that was ended quickly by being snatched and placed into slavery, his story is a reflection of one within many stories that are no doubt similar in fashion. The most memorable, and possibly disturbing narration involves his experiences within the slave ship.
...at his favorite place has changed with time. This change with time and the experience one gets from such changes allows the reader to think about how and why things change when you least expect it and how time progresses with or without you.
For millions, fast food restaurants are the source of positive associations with birthday parties, play dates and accessible comfort food. For others, they represent a lifeline meal on a busy day, or the secret to quieting a cranky toddler on a long trip because hurrying residents of cities have no time to cook a healthy breakfast, lunch and dinner. Fast food presents even in the lives of people who are trying
The Norton Anthology of English Literature. Sixth Edition Volume1. Ed. M.H.Abrams. New York: W.W.Norton and Company, Inc., 1993.
Statistic images and landscapes, or know as fractal landscapes, and the way that this component works is that these statistic images...
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".