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FRACTAL

FRACTAL. GEOMETRY. Amgad Hussein, Maria Tokarska , Edward Grinko , Dimitar Atassanov , Megan Varghese, Emilio Asperti. What is Fractal Geometry?.

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FRACTAL

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  1. FRACTAL GEOMETRY Amgad Hussein, Maria Tokarska, Edward Grinko, DimitarAtassanov, Megan Varghese, Emilio Asperti

  2. What is Fractal Geometry? • "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” – Benoit Mandelbrot • Fractals are geometric figures, just like rectangles, circles and squares, but fractals have special properties that those figures do not have. • They are mathematical hydras that replicate themselves by fragmentation

  3. Properties of Fractals • Fractal patterns come in infinite varieties • One property is being very crinkly. Being crinkly means that very long lines and very large areas have a structure that fits them into very small spaces. • Another essential quality of fractals is self-similarity on very different scales: a small piece of the Dragon has the same general pattern as does a large piece of the dragon. • These two qualities are also commonly found in nature, and there are many references to fractals in nature.

  4. Fractals in Nature • The Human Circulatory System: If all of the veins, arteries and capillaries in an adult human were laid out end-to-end, then the total length would be over 50,000 miles long!That is lots of crinkliness. • Also, small branches of a tree have the same patterns, same angles and shapes as large branches of the same tree. Sounds like a fractal to us! • Similarly, it is not hard to find a rock with small scale fractures, lines, bumps and patterns that have the same form as the large scale fractures, lines, bumps and patterns on the formation of which the rock is a part. SO fractally!

  5. Fractalian Careers • Architects • Fashion Designers • Animation people • Mathematicians (duh!) • Engineers

  6. Mandelbrot Sets • A mathematical set of points whose boundary is a distinctive and easily recognizable two dimensional fractal shape • Images of the Mandelbrot set are made by taking numbers on the complex plane, calculating whether it tends to infinity when the formula is iterated on the number, then using the number as X and Y coordinates in the picture and coloring the pixel depending on whether it tends to infinity or not.

  7. Julia Sets • the set of points which do not approach infinity after is repeatedly applied • consists of values such that an arbitrarily small modification can cause drastic changes in the sequence of iterated function values.

  8. Jurassic Park Fractal • We know you saw the movie, but did you read the book? Did you notice the bizarre drawings on the chapter heading pages? That’s right, those were Jurassic Park Fractals • Now we, as a class, will make the Jurassic park fractal • ENJOY!

  9. SIMULATION • http://cs.unm.edu/~joel/PaperFoldingFractal/paper.html

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