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Fractals

Interactive fractals

The Fractal explorer below will zoom in on a given section chosen by YOU of the Mandelbrot Set.

The explorer will recalculate the given output for every new input and show you how Fractals continue forever into infinity.

What is a fractal?

A fractal is usually a rough or broken geometric shape which can be subdivided into parts.  A fractal is the result of the input and output of a formula in a special software program.

Fractals, described by Benoit Mandelbrot, is any image that is infinitely complex and self-similar at different levels. This is one definition of a fractal. A commonly used definition is something whose area is finite but whose perimeter is not.  Many fractals involve complex math.

Many computations of fractals involve complex numbers. Complex numbers are numbers with imaginary parts, which are in terms of "i" and a real number. "i" equals the square root of -1. Therefore, a complex number is often defined as a+b*i, where "a" and "b" are real numbers. To understand why this is necessary, try to compute the square root of negative one on a calculator, and see that it isn't possible with normal real numbers. To deal with this problem, mathematicians simply invented the quantity "i" to represent this. Complex numbers follow their own rules that sometimes differ from those of real numbers. Because of their unique properties, they are often used in fractals that are graphed in the complex plane, where the real number axis (a) lies horizontally and the imaginary axis (b) lies vertically. The Mandelbrot set is one example of a fractal that is graphed in the complex plane.

How to use the Mandelbrot Set Explorer below:

 INPUT:  Draw a rectangle within the Mandelbrot image (see example - right).  Then click "Go!"OUTPUT:  You'll get an amplification of the area inside the rectangle you created. Click the "col+" and "col-" buttons to change the color table. The In and Out buttons let you zoom in and out through the explored regions. Explore the border between colored areas and the black set. The (Benoit) Mandelbrot Set Explorer

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"Fire @ F-Holes Cove"
Blue Ridge Reservoir, AZ
September 4, 2007