Saturday, October 6, 2012

The Sierpinski Triangle

     The work of Waclaw Sierpinski, a Polish mathematician, is now associated with fractal geometry. In 1915 he created what is referred to as the Sierpinski Triangle (Mandelbrot,1977). This triangle demonstrates some of the unusual mathematical concepts that are found in fractal geometry.
   To begin, one must draw an equilateral triangle and then bisect each side. Lines are drawn, connecting the midpoints. A new triangle is formed inside the original creating four triangles within the original. All sides are bisected and joined.

This is a Sierpinski Triangle used as a color wheel by one of my students. 

The amazing fractal think about this triangle is that the length of the perimeters of the triangles are approaching an infinite length while the area approaches zero. 

     I first heard about fractals by listening to NPR. One I looked them up I was hooked on their beauty As I continued to research fractals I found out there was a lot to know.
     The first thing to know is that fractals come from fractal geometry whose 'father' is Benoit Mandelbrot. There were former mathematicians that had ideas that helped lead to fractal geometry, but it was Mandelbrot who put it all together in the early 19702..
     Three of the early mathematicians to know about are Sierpinski, Koch and Julia.

What is the void?

     Who ever talks about fractals and how to create them? Generally, a few people who have complicated software talk about creating fractals. How to create a fractal without software or complicated math is a void. No one talks about those things, except me.
    The intent of this site is to talk about what fractals are, how to identify them and most importantly ways to create your own fractals by hand.
     Please join me on this quest to fill the void and talk to me about fractals. They are my passion.