The Color Scheme is the fundamental way that colors are chosen for
each pixel to render a graphical image after the fractal equations
are calculated. Two color selection methods are used by
Fractals and these are called Convergence and Divergence.
Without getting too much into the technical details of how this is
done, here's a brief explanation of what Convergence and Divergence
mean.
The fractal calculations are done as a series of iterations on the
XY coordinates of each pixel in the image. The result of each
calculation is a new set of XY coordinates somewhere in magical
XY space. The new coordinates may or may not be within the bounds
of the image.
With the Convergence method, the distance between the old
coordinates and the new coordinates is calculated at every iteration.
If the distance is less than the selected Convergence Limit, the
pixel has converged and no more calculations are done on it.
In other words the pixel has settled down to a very small
area and isn't going to move any more so we don't want to do any more
calculations. The number of calculations that were done to get to
that point are counted and kept track of.
With the Divergence method, the distance from the center of the image
to the new coordinates is calculated at every iteration.
If the distance is greater than a fixed number based on the image
size, the pixel has diverged and no more calculations are done on it.
In other words the pixel has left the playing field and isn't coming
back, so we don't want to do any more calculations. Again as with
Convergence the number of calculations that were done to get to
that point are counted and kept track of.
Now, keeping in mind how these numbers are calculated, read about the
Color Palette to see how they are used to
assign a color to each pixel.
A few other things to know about the Color Schemes...there are two
Convergence choices for the Color Scheme, Convergence A and Convergence
B. Convergence B is an interesting variation of the typical convergence
scheme.
If you experiment with it you will find that it tends to "fracture" parts
of the image when compared to Convergence A. There's not much more to
say about it without going into mathematical details, so here's an example
of both color schemes used with
GoldenBrot from the Fractal Gallery:
Color Scheme = Convergence A

Color Scheme = Convergence B

Also, the Convergence Limit is only used with the Convergence
schemes and not for Divergence.
Basically the Convergence Limit value is used in an inverse power of
2 relationship (i.e. limit = 1/2^{n}). What does that mean?
It means that the larger the control value is, the smaller the
distance between coordinates on successive iterations must be to satisfy
the convergence criteria. It's not really important to understand this,
just that the tendendency is for the image detail to get more complex
as the Convergence Limit number gets larger.
Here's an example of Flutter By
from the Fractal Gallery with two different convergence limits:
Convergence Limit = 4

Convergence Limit = 6

