What is a FRACTAL?
Wolfram MathWorld says a fractal is an object or quantity that displays self-similarity.
When you examine any small corner of the picture to the left, it looks almost exactly like the bigger picture.
Try zooming in at any spot on the Mandelbrot Set to see the similarity with the original picture.
What is ITERATION?
Iteration is a repetition of an operation or process. After you perform the operation on the initial input value, the operation is repeated on the result, then the operation is repeated on that result, and again, and again . . .
Check out what Dr. Math on The Math Forum says about Iteration
(ALSO, Dr. Math is a great place to go when you have unanswered MATH QUESTIONS)
Would you like to create a fractal yourself? Check this out to create a fractal!
Fractals look cool, but there's so much more to know about them. Young Mathematicians can learn about fractals at this Fractal website.
Did you know that fractals have applications in medicine, science, industry and nature? Click here to learn about some applications of fractals.
Check out this Investopedia article about applying fractals to investing.
Fractals as art:
The Sierpinski Triangle is formed by drawing lines that connect the midpoints of the sides of an equilateral triangle. This forms four smaller triangles, with the triangles at the original vertices colored and the middle one left uncolored. This is iterated (performed over and over again), creating smaller and smaller triangles that are colored in a similar manner.
The slide show below shows a number of examples of the Sierpinski Triangle.
The picture at the left shows a more creative manifestation, aptly named the "Sierpinski Coke."
The slide show below shows a number of examples of the Sierpinski Triangle.
The picture at the left shows a more creative manifestation, aptly named the "Sierpinski Coke."
Fractals inspire:
Some students at Alexander Hamilton School in Cleveland, Ohio were inspired to create the world's largest tetrahedron, using the Sierpinski Triangle.
The work of these students inspired author Shelley Pearsall's book, All of the Above, a story that includes and goes beyond four inner-city students' quest to set the world record for largest tetrahedron.
The work of these students inspired author Shelley Pearsall's book, All of the Above, a story that includes and goes beyond four inner-city students' quest to set the world record for largest tetrahedron.