What is a fractal?

See http://fractalfoundation.org/ for much more information and even a fractal course

Alan Beck writes:

"Basically, a fractal is any pattern that reveals greater complexity as it is enlarged. Thus, fractals graphically portray the notion of 'worlds within worlds' which has obsessed Western culture from its tenth-century beginnings."

Power Point Introduction to Fractals

http://mathforum.org/alejandre/workshops/fractal/fractal3.html

http://mathworld.wolfram.com/Fractal.html

http://classes.yale.edu/fractals/

History of Numbers and Fractals

Calculus Invented simultaneously by Newton and Leibniz

For 200 years mathematicians tried to prove calculus rigorously

During that time mathematicians like Koch, Cantor and Sierpinski found curves that had no tangents

Space Filling Curves - hidden in closet

Benoit Mandelbrot found the connection between all of these curves

Fractals were born

Why Study Fractals?

http://math.rice.edu/~lanius/fractals/WHY/

What is Sierpinski's Triangle?

http://math.bu.edu/DYSYS/chaos-game/node2.html

Interactive Triangle generated by the chaos game

http://serendip.brynmawr.edu/playground/sierpinski.html

How do You make a Sierpinski Triangle?

What is Sierpinski's Tetrahedron?

Pictures -           http://makezine.com/2012/06/25/math-monday-tetrahedron-ripples/

http://www.public.asu.edu/~starlite/sierpinskitetrahedron.html

templates and blackline masters

http://math.fau.edu/Teacher/CATEs_PDF/3%20sierpinski/sierpinski%20unit%204.pdf