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 x-coordinate while b acts as the y-coordinate. 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.
|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:
is what the latter formula means:
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