FRACTAL GEOMETRY INTRODUCTION Fractals is a new branch of mathematics and art. Most physical systems of nature and many human artifacts are not regular geometric shapes of the standard geometry derived from Euclid (i.e‚ Euclidian geometry: comprising of lines‚ planes‚ rectangular volumes‚ arcs‚ cylinders‚ spheres‚ etc.) Fractal geometry offers almost unlimited ways of describing‚ measuring and predicting the natural phenomena. “Why is geometry often described as ‘cold and dry’? One reason lies
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Fractals Introduction Fractals are geometric patterns that when repeated at increasingly smaller scales they produce irregular shapes and surfaces. All fractals have a feature of ‘self-similarity’. A set is self-similar if it can be broken into arbitrary small pieces‚ each of which is a small copy of the entire set‚ for fractals the pattern reproduced must be detailed (Nuhfer 2006). Self-similarity may be demonstrated as exact self-similarity meaning the fractal is identical at all scales a fractal
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Fractals have been one of the tools used in Euclidean geometry to explain the abnormal shapes in nature. Fractals are able to explain the irregular shapes that are a far cry from the normal circle or square. It is an object of symmetry that uses components to create the picture of a self-similar entity. Fractals first appeared on the scene in 1918 due to the mathematician‚ Felix Hausdroff. A Poland mathematician by the name of Beniot B. Mandelbrot began the term fractals. Fractals originated from
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FRACTAL TIME (ESSAY) Introduction In his book‚ first published in 2009‚ ’Fractal Time: The Secret of 2012 and a New World Age’‚ Gregg Braden gave wonderful clues into what we would expect to occur in our world and universe by the year 2012. Though years have passed since the first publication of the book‚ the information in the book remains relevant to us today. Gregg labours to elaborate how it is possible to read the past in order to discover what the future holds for us in our world and
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Fractal Geometry "Fractal Geometry is not just a chapter of mathematics‚ but one that helps Everyman to see the same old world differently". - Benoit Mandelbrot 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
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Fractal Geometry How would you like to take a class called geometry of chaos? Probably doesn’t sound too thrilling. A man named Benoit Mandelbrot is responsible for creating the geometry of chaos. The geometry of chaos is considered to be the fourth-dimension. It is considered to be the world in which we live in‚ a world where there is constant change based on feedback‚ an open system where everything is related to everything else. It is now recognized as the true geometry of nature. The geometric
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is also no doubt that patterns are just as mysterious as they are beautiful. In fact‚ there are some patterns that are so perfect that they self-replicate. To be technical‚ some patterns are fractal in nature. Fractal or not‚ patterns give us something more to admire and wonder about. Introduction Fractals never fail to fascinate. If you aren’t just gazing at their unearthly beauty‚ you ponder the mathematics behind them... and then you can’t help but wonder how such prosaic‚ unsensational mathematical
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with fractal architecture as one of the defining solutions for the contemporary complex urban fabric. SUBMITTED BY: Lily Tandon SEMESTER:VIII CHAPTERS 1. The End Of The Modern World 2. What abstraction does 3. From the modern to the complex 4. From complexity to form generation 5. Form generation and fractals 6. Fractals
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According to Williams‚ a trader must first know himself then know the market. By examining the market‚ traders can see self-repeating patterns. They also find the Golden Ratio‚ 0.618‚ revealed by the Fibonacci sequence. A fractal is a unit of measure of irregularity. Fractal dimension means that people look at things as one dimensional from afar. But‚ people recognize that things are three dimensional as they get closer. Market chaos have negative connotations. People filter some things out of
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Introduction The birth of every technology is the result of the quest for automation of some form of human work. This has led to many inventions that have made life easier for us. Fractal Robot is a science that promises to revolutionize technology in a way that has never been witnessed before. The principle behind Fractal Robots is very simple. You take some cubic bricks made of metals and plastics‚ motorize them‚ put some electronics inside them and control them with a computer and you get machines
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