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A fractal fractal is a mathematical object that exhibits self self similarity similarity — it looks the same at any scale

Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

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Page 1: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

A fractalfractal is a mathematical object that exhibits self self

similaritysimilarity — it looks the same at any scale

Page 2: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

Benoit MandelbrotProfessor of Mathematical Sciences

Yale University

Coined the Coined the word “fractal” word “fractal” in 1975in 1975

http://www-gap.dcs.st-and.ac.uk/~history/PictDisplay/Mandelbrot.html

Page 3: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

Fractal Sequence:• A fractal sequencefractal sequence contains an infinite number of copies of

itself, embedded within itself.• It is a pattern within a pattern within a

pattern

Page 4: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

• Fractals are often formed by what is called an iterative process

• to repeat exactly the same step over and over

Page 5: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

• Fractals are often formed by what is called an itertive process

• to repeat exactly the same step over and over

Page 6: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale
Page 7: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

Mathematics & Science Center

By: Corey Kisner and Cari FaszewskiBy: Corey Kisner and Cari FaszewskiMay 18, 2000May 18, 2000

Sierpinski Carpet

Page 8: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

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Eight Tangent Reflecting Spheresby Dave Matthews

2004

http://astronomy.swin.edu.au/~pbourke/povray/povfrac/final/

Page 9: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

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Page 10: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

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Page 11: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

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Page 12: Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale

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