How do you generate a fractal?
Fractals are
generated using formulas which contain a complex number. These formulas are iterated, then they are
"graphed", usually on a complex plane. The formulas are shown
below.
How do you "graph" the results from a iterated formula?
After each iteration in a formula, you are given
two main numbers to act as your "x and y" coordinates.
Since a complex number is used, a will act as the xcoordinate
while b acts as the ycoordinate. As you continue to iterate the formula,
you have new coordinates to plot. After iterating various times, you
produce a series of lines. This is where a rather
sophisticated computer is needed. Since it is impossible to graph an
imaginary number, the computer that is used must be able to graph these coordinates
and interpret these lines.
Basic iteration formula You must define f(x) to apply this formula. GENERAL FORMULA:

Most commonly used iteration formula
(derived from the basic iteration formula): You must define c to apply this formula. c will always be a complex number. There are limitations for a and b: 2.5<a<1.5 1.5<b<1.5 GENERAL FORMULA: This
is what the latter formula means:

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