Fractals
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Transcript of Fractals
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Fractals
What are fractals?
Who is Benoit Mandlebrot?
How can you recognize a fractal pattern?
Who is Waclaw Sierpinski?
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What are fractals?
A fractal is a pattern that is self-similar. When magnified, small parts of a self-similar figure cannot be distinguished from the whole figure.
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Benoit MandelbrotBenoit Mandelbrot was born
in 1924 in Warsaw and moved to the US in 1958. He is known as the “father of fractals. He is a mathematics professor and researcher. He made many important discoveries in the field of fractals during the 1970’s and 1980’s. In 1982 he connected mathematics and nature through fractal geometry.
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Fractals in NatureSome natural objects
that approximate fractals include:
Clouds
Mountain ranges
Lightning bolts
Snowflakes
Broccoli & cauliflower
Crystals
Trees and ferns
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Waclaw Sierpinski1882-1969
Waclaw Sierpinski was born in 1882 in Warsaw, Poland. He was a professor of mathematics at the University of Lvov, the University of Moscow, and the University of Warsaw. He invented the Sierpinski Gasket.
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The making of a Sierpinski Gasket
1. Take your equilateral triangle and find the midpoint of each side. Connect the midpoints. (Stage 1)
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The making of a Sierpinski Gasket
2. Find the midpoint of each side of the three outside triangle and connect the midpoints. (Stage 2)
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The making of a Sierpinski Gasket
3. Find the midpoint of each side of the nine outside triangle and connect the midpoints. (Stage 3)
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Creating a Fractal Card
Step 2 Step 3 Step 4 …
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Fractal Construction
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Fractal Figures
Let’s look a making some other fractal figures.
http://www.hbschool.com/activity/elab2004/gr6/21.html
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Van Kock Curve
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Lines Fractal
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Julia Phoenix
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Pentagon Fractal
http://www.coolmath.com/fractals/gallery.htm
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• What are fractals?
A fractal is a pattern that is self-similar. When magnified, small parts of a self-similar figure cannot be distinguished from the whole figure.
• Who is Benoit Mandlebrot?
He is known as the “father of fractals.
• How can you recognize a fractal pattern?
When magnified, small parts of a self-similar figure cannot be distinguished from the whole figure.
• Who is Waclaw Sierpinski?
He invented the Sierpinski Gasket (triangles in triangles).