What's the Big Deal About This Fractal Then?

	The Yankovic set is not just a different variation on an old theme,
it's a new approach to drawing the famed Madelbrot Set, and it has totally
unpredicted results.
	The Yankovic set is the Mandelbrot Set's evil twin brother. The
program shown here which draws the set was originally designed to draw the
Mandelbrot Set, so they both are built off a similar system and use the same
equation [f(z)->z+c, where z is c plus a constant, and c is the solution
from the last iteration of the equation] to draw itself. However, because
QBasic (the original language I wrote it in. Since, I have gone to Quick
Basic, which is a whole helluvalot faster) is so slow I chose to, instead of
testing every point on the screen to see of it belonged to the equation, 
tell the computer to draw the equation as it came along, and only test the
points that produced a solution (fractals that are drawn this way are known
as dynamically rendered). Instead of drawing the Mandelbrot set, the program
instead drew what is now called the Yankovic set.
	Before beginning, let me explain one of the irritating idiosyncrasies
of the Yankovic set: the snow. If you look at any of the pictures of the set,
you will see around and about the set tiny spots of color, which look sort of
like stars against the black background. The reason that these "stars" exist
is because of the way the set draws itself. The set consists of many
different curves, each of which is visable at a different level of detail.
You will notice that on the same picture of the fractal, some of the curves
in the set are smooth and contiguous, while others are broken and have wide
spaces between the pixels that make them up. The "stars" in the Yankovic set
are points on curves that have such large gaps between the pixels in each
curve that it is impossible to tell that they are even part of a curve.
Turning up the resolution doesn't help, because then you get snow from curves
that had such wide spaces between each pixel that you couldn't tell that they
were there at all until you turned up the resolution. However, precise detail
control can eliminate the most distracting snow by not doing the high detail
rendering until the fractal has reached the part you want to see.
	The Yankovic set, as fractals go, is weird. In most fractals,
the black areas of the equation's graph are points that belong to the set,
and the colored areas are not (the colored areas are colored according to how
many times the computer has to try to solve the equation with the point in
question before it decides that the point is not part of the equation). The
same goes for the Yankovic set, so it would seem that most solutions satisfy
the Yankovic set, which is extremely bizarre for a non-linear equation of any
kind, imaginary or not. However, after watching the set iterate at many
different resolutions, it seems that eventually the screen would fill with
color if I could turn the resolution up high enough, so really, there is no
soultion!
