##Team members:
Tianpei Luo;Dillon Guarino;Matthew Melachrinos
##What is a Mandelbrot set?
A mandelbrot set is a set of complex numbers that when graphed, form self similar patterns called fractals. Technically speaking, the mandelbrot set is “the set for which fc(z) = z2+ cdoes not diverge when iterated from z=0. When iterating the function, one of two things can happen. Either z grows to infinity, it “blows up” so to speak, or it stays bounded within r = 2. The mandelbrot set is the set of all numbers that stay bounded.
##Our Goals
Our goal, simply put, is to create efficient algorithms for generating mandelbrot sets to a large degree of detail in a fast way for the high iterations. This is a great project for an algorithms class because a brute force approach to this problem would be terribly slow. This leaves a large opportunity to develop better algorithms.
##Our Approach
First, we will develop a brute force algorithm. This serves two purposes. First, it helps us learn more about Mandelbrot sets. It also gives us a baseline to measure our later algorithms against. It’s commonly said that you can’t know happiness without knowing sadness. Similarly, you can’t know a good algorithm unless you know a bad one.
Second, we’ll build Mandelbrot sets using parallel calculations. Generating the set is a great opportunity for parallelism because you can start iterating from many different starting points at the same time.
Finally, pending time constraints, the group will work on visualizing these sets. A simple set of numbers is not particularly interesting, especially in comparison to the beauty found in a visualization of these sets. However, this is not core to the project since it is an exercise in c++ programming not algorithm development. Ideally, a module will be found online that can be imported into the project that will display the sets generated from the projects algorithms.
##References
https://en.wikipedia.org/wiki/Mandelbrot_set
http://mathworld.wolfram.com/MandelbrotSet.html
https://www.youtube.com/watch?v=NGMRB4O922I
http://www.fractalforums.com/programming/newbie-how-to-map-colors-in-the-mandelbrot-set/