Fractals: The Organization of Chaos
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Fractals are a relatively new concept in geometry. Most concepts for Euclidean geomtery, the division of geometry which deals with lines, circles, triangles, and other standard shapes, stem from the Late Greek and Early Rioman times. Considering the age of mathematics, the study of fractals is new becasue it dates to the beginning of this century. However, the age of computers brought about an explosion into this yet untamed universe of math. As Heinz-Otto Peitgen and Dietmar Saupe remark in the preface for The Science of Fractal Images, "Computer graphics has played an essential role both in its development and rapidly growing popularity" (V). Before this, mathematicians could only visualize what they were discussing (Mandelbrot, Fractals: Form, Chance, and Dimension 2). But now, fractals are the mathematician's answer to chaos and therefore can be used to help scientists better understand nuature and the universe. Scientists can define any structure from a snowflake to a mountain or even an entire planet with this new division in Mathematics. Thus, fractals define our universe.
Benoit B. Mandelbrot is a key figure behind the rise of this new science. A Professor of mathematical Sciences at Yale and an IBM Fellow, Mandelbrot is the man who coined the term "fractal" in 1975. Mathematicians, such as Gaston Julia, only defined them as sets before this and could only give properties of these sets. Also, there was no way for these early fractal researchers to see what they were hypothesizing about. As Mandelbrot states in The Fractal Geometry of Nature, "I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means 'to break...'" (4). Mandelbrot used this particular root because of how he defines fractals. Unlike Euclidean geometry, which has its figures in a particular dimension (e.g. a square is two-dimensional), fractals have fractional dimensions. They do not exist in just one dimension but can encompass part of another. For example, as Mort La Brecque states in his article on fractals in the Academic American Encyclopedia "a natural fractal of fractal dimension 2.8 ... would be a spongelike shape that is nearly three dimensional in its appearance. A natural fractal of fractal dimension 2.2 would be a much smoother object that just misses being flat" (105-106, Mandelbrot "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.
“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.
The data from World Health Organization (WHO) on the leading causes of death worldwide and the global burden of diseases shows that, traumatic injuries are the major cause of mortality, morbidity and disability among children (0 – 14 years) - being responsible for more deaths than the combination of other diseases1. It is against this backdrop that pre-hospital care during emergencies becomes very important in the management of the injured children as it is for adults. In most circumstances, earliest responder who could be a medical doctor, paramedic, or even layman are the first to provide the much needed life saving (basic or advance), vital medical care all with the aim of optimizing the victim’s physiological status prior to arriving nearest medical facility2, 3. Indeed, several evidences suggested that these first life-saving supports have effect on the morbidity and mortality of the injured patient2-4. But, recent researches have also shown that interventions like invasive airway management, IV access and fluid administration are associated with higher rate of complication and failure among paediatric patients, while the few that turned out to be successful were provided by specially trained and experienced personnel3. This is due to the difference in size and overall anatomy of children compared with adult, thus many of these procedures turn out to be difficult or results in complication when performed...
The Fibonacci numbers are a sequence of numbers that begin with 0, 1 ... and then calculated each number from the sum of the previous two. The equation for this method is . Another theory he studied was a sequence that has a flower like pattern. Fibonacci's second work was the Practica geometriae and was composed in 1220-1221. The Practica geometriae draws heavily on the works of the ancient Greek masters i.e. Plato. Fibonacci made a dent in mathematics history.
David W Lesch, Mark L Haas. The Arab Spring: Change and Resistance in the Middle East. Westview Press, 2012.
Barrie presents Mr. Darling as the worker of the family, a proud businessman. He persistently demands respect and obedience from his wife, children, and Nana the dog. As well as this, he boasts to Wendy that Mrs. Darling not only loves him, but respects him. This outlook is linked to the stereotypical view of the male gender as the main source of income, with a resilient disposition and a necessity for order. When Mrs. Darling talks to him about Peter Pan, he dismisses her concerns, suggesting indifference and a lack of concern for others’ views.
Hansen, M., ABA Journal. Jul97, Vol. 83 Issue 7, p20. 2p. 1 Color Photograph, 1 Chart.
Gerner, Deborah J., and Philip A. Schrodt. "Middle Eastern Politics." Understanding the contemporary Middle East. 3rd ed. Boulder, Colo.: Lynne Rienner Publishers, 2008. 85 -136. Print.
Big Data is a term used to refer to extremely large and complex data sets that have grown beyond the ability to manage and analyse them with traditional data processing tools. However, Big Data contains a lot of valuable information which if extracted successfully, it will help a lot for business, scientific research, to predict the upcoming epidemic and even determining traffic conditions in real time. Therefore, these data must be collected, organized, storage, search, sharing in a different way than usual. In this article, invite you and learn about Big Data, methods people use to exploit it and how it helps our life.
Palumbo, Donald. "The monomyth as fractal pattern in Frank Herbert's Dune novels". Science Fiction Studies 25.3 (Nov. 1998): 433-58.
Big data analytics is the process of extracting meaningful data out of a Big Data so that predictions can be made, or events can be correl...
Big data originated with web search companies that encountered problems with querying large amounts of both structured and unstructured data. With regard to its background, “big data came into being when web search companies developed ways to perform distributed computing on large data sets on computer clusters” Floyer (2014: 1). Big data then spread to enterprises due to their adoption of developing, processing and dissemination of data.
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.
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.