It can be used to make windows and text, and provides the capabilities for a lot of variation within viewpoints, and plotting. Our first program was to try simply drawing a window with a less common graph. The next challenge was to incorporate mouse or keyboard control into the program. I wasted some time to create a program with a 9-window display, each of the windows acting as a button. Finally, a step in the mathematical thinking behind the programming was needed for the next program.
Bifurcation works as follows.
The 'web' of lines show the different iterations being graphed. The first terms of these equations can be easily derived from the squaring of complex numbers. The addition of a0 and b0 are what separates the calculation of the Mandelbrot Set from the Julia Set. In the Mandelbrot Set, the original point is added to the squared point whereas in the Julia Set, a chosen point is used as the added points for all points tested. After the given number of itterations, and also through the loop, the distance of thise 'squared' point is checked against a distance of 2.