Mathematics Science Fair Project
Variable values effect on fractal Mandel equation calculation time

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Project Information
Title: Determine if changing the variable values of the fractal Mandel equation would change its computer calculation time.
Subject: Mathematics
Grade level: Elementary school - grades 4-6
Academic Level: Ordinary
Project Type: Experimental
Cost: Low
Affiliation: Selah Junior High School
Description: FractInt (a freeware software package that can render and display many kinds of fractals) was used to calculate the Mandel fractal by changing variables; caculation time was recorded and graphed.

Mandelbrot Set

The Mandelbrot set (black) within a continuously colored environment
Wikimedia Commons / Wolfgang Beyer / CC 3.0 GNU 1.2

The Mandelbrot set, named after Benoît Mandelbrot, is a famous example of a fractal. The Mandelbrot set is a mathematical set of points in the complex plane, the boundary of which forms a fractal. It begins with this equation: zn+1 = zn2 + c. Starting with z0=0, c is in the Mandelbrot set if the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets.

For example, if c = 1 then the sequence is 0, 1, 2, 5, 26,…, which goes to infinity. Therefore, 1 is not an element of the Mandelbrot set.

On the other hand, if c is equal to the square root of -1, also known as i, then the sequence is 0, i, (−1 + i), −i, (−1 + i), −i…, which does not go to infinity and so i belongs to the Mandelbrot set.

When graphed, the Mandelbrot set is very pretty and recognizable.

See also: Mandelbrot Set

Source: Wikipedia (All text is available under the terms of the Creative Commons Attribution-ShareAlike License)

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