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Fractal (Math)

            
             Many people have seen or heard of fractals, but not many people actually know what they are. The answer to the question "What are fractals?" is really simple. Fractals can be anything that contains self-similar images within itself. For example, the human.
             Circulatory system is a fractal. If you look at the blood vessels in your hand, they resemble the overall shape that the complete system takes on. We are constantly surrounded by fractals and most people don't realize it. A majority of the fractals you see.
             in the world today self occur. Which means humans did not construct them. I would now like to discuss the computer-generated fractals like those that you would find in the Bare Fractals and Fractal Art sections like you might see in a museum.
             Computer generated fractals are created using geometry. A mathematician would tell you that fractals are created at the boundary between chaos and order. To fully understand fractals, one must understand the chaos theory. The theory states that everything is subjected to so many variables that it becomes almost, but not completely, random. A meteorologist named Edward Lorenz helped to pioneer the study of chaology in the 1960's. Using a simple system of equations to model convection in the atmosphere, he ran headlong into "sensitivity to initial conditions". In the process he sketched the outlines of one of the first recognized chaotic attractors. In Lorenz's meteorological computer modeling, he discovered the underlying mechanism of deterministic chaos: simply-formulated system with only a few variables can display highly complicated.
             behavior that is unpredictable. Using his digital computer, slashing through reams of printed numbers and simple strip chart plots of the variables, he saw that slight differences in one variable had profound effects on the outcome of the whole system. This was one of the first clear demonstrations of sensitive dependence on initial conditions.


Essays Related to Fractal (Math)

1. Math In Everyday Life

... Project for K-12 , students learn how the stock market works and discover how factors, such as company management, politics, weather, and other variables, affect it. In the unit's math lessons, students calculate commissions and odds, compare price-to-earnings ratios, use fractions and decimals, graph the results of various investment strategies, and more. The project's Teacher Resources reference ... includes a For Teachers section, featuring suggestions for using Moneyopolis as an educational resource, ideas for off-line educational activities, sample lesson plans, and explanations of t...

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2. Math in Art

Throughout history, thinkers from mathematicians to artists have pondered the mysterious relationship between number and form. This relationship is captured in many ancient works of art such as the Parthenon of Greece, the Pyramids, and also in more recent works like Leonardo Da Vinci's Mona Lisa. Mathematical proportions have been conveyed in many forms of art, architecture, music, and nature that bring beauty, order and mystery to people and cultures everywhere. Looking into the past, through the millennia, we can see the use of these proportions and ratios emerge. The use of mathematical to...

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3. Fractals

... is short for fractal dimension, is a branch of math that deals with irregular patterns made of parts that are in some way related to a whole. Some examples of this are twigs or tree ... branches and a property called self-similarity or self-symmetry. This is different from conventional geometry, which deals with regular shapes and whole-number dimensions. Examples of this are lines and cones. Fractal ... such diverse fields as the stock market, chemical industry, meteorology, and computer graphics. He proposed the idea of a fractal as a way to cope with problems of scale in the real wor...

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4. Origami

... curvature in a hyperbolic paraboloid. Origami also abounds with accessible open problems that give students a chance to contribute original ideas. Many students who have not previously experienced success in math flourish after a well-crafted unit involving origami. Origami provides a nice link to topics in other parts of the curriculum and can give students a reason to want to learn ... field, mathematicians are already investigating a wide range of questions relating to paper folding. Some of these investigations try to design, classify, or find colorings for origami polyhedra, tessell...

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5. Hearts

... has given birth to a handful of new branches in mathematics, including abstract algebra, transformational geometry, and topology. The 19th century is the source of numerous advances in calculus, algebra, and (fractal) geometry. In the 1840s George Boole and Gottlob Frege establish the science of measurement, symbols, and numbers thru the use of algebra. This science is now known as symbolic logic ... new ideas. There are many opportunities in mathematics. Mathematicians may choose to start a career in teaching. The two most widespread areas of opportunity in math are called theoretical ...

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