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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Fractals. What are fractals? Who is Benoit Mandlebrot? How can you recognize a fractal pattern? Who is Waclaw Sierpinski?. 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. - PowerPoint PPT Presentation
Transcript of Fractals
Fractals
What are fractals?
Who is Benoit Mandlebrot?
How can you recognize a fractal pattern?
Who is Waclaw Sierpinski?
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.
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.
Fractals in NatureSome natural objects
that approximate fractals include:
Clouds
Mountain ranges
Lightning bolts
Snowflakes
Broccoli & cauliflower
Crystals
Trees and ferns
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.
The making of a Sierpinski Gasket
1. Take your equilateral triangle and find the midpoint of each side. Connect the midpoints. (Stage 1)
The making of a Sierpinski Gasket
2. Find the midpoint of each side of the three outside triangle and connect the midpoints. (Stage 2)
The making of a Sierpinski Gasket
3. Find the midpoint of each side of the nine outside triangle and connect the midpoints. (Stage 3)
Creating a Fractal Card
Step 2 Step 3 Step 4 …
Fractal Construction
Fractal Figures
Let’s look a making some other fractal figures.
http://www.hbschool.com/activity/elab2004/gr6/21.html
Van Kock Curve
Lines Fractal
Julia Phoenix
Pentagon Fractal
http://www.coolmath.com/fractals/gallery.htm
• 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).
