Math Research Paper on Fractals

Essay by RuzebHigh School, 10th gradeB, April 2013

download word file, 10 pages 0.0


A fractal created with the Julia set under constant -.74434 - .10772i.

The mathematics behind fractals, such as the Koch Curve, is rather simple, yet it becomes a complicated, yet ingenious method when referring to the Mandelbrot Set.

In order to create a fractal, you will need to be acquainted with complex numbers. Complex numbers on a graph are characterized by the coordinates of (x,y) in which the x-coordinate is any rational number, whereas the y-coordinate contains an imaginary number, denoted by "i". An imaginary number is the square root of a negative number. An example of a complex number can be: (5 + 4i).

Complex numbers look ambitious, but they are not. In order to add complex numbers, you just need to add like terms:

If you are faced with i2, please note that it is equal to -1!

We shall start with Mandelbrot's set. The Mandelbrot set was popularized due to...