##
What is a fractal?

B. B. Mandelbrot calls *fractal*
(from latin *frangere *i.e. to break) a very complex structure that
looks like itself at any level of detail.
Often such structures show an underlying
geometrical regularity, called *invariance *w.r.t. scale change or
*self-similarity*, that seems to describe natural shapes and configurations
in a better and more synthesised way than traditional Euclidean geometry.

One way for building fractal images
is to apply the concept of *iteration*, by computing a sequence of
points in the complex plane, defined as follows by a function *f*:

#
*z
n+1 = f
(z n)*

Many natural phenomena can be described
by mathematical models of this kind. The evolution of a population, the
behavior of the atmosphere and the growth of a capital are just a few examples.

##
**
**How can one draw a fractal?

In order to draw a fractal one must
decide how to assign colors to the points in the plane. There are different
ways of doing it, one is the following. Given a point *Z* in the plane,
a function *f*, and a value for the constants in* f* , one starts
an iterative process in which, first, *f *is applied to *Z *and,
subsequently, to the result of the previous iteration. The color of the
point *Z *will be decided depending on the *number of iterations*
produced before *f *'s value grows higher than a predefined threshold.
Observe that different images of
a same fractal can be obtained simply by changing the function *f *and
the color palette.