Fractals most usually are of the complex form of numbers, Real & imaginary.
Real numbers can be thought of as the value of length of side of square with positive Area.
Imaginary numbers are value of length of side of square of negative Area
The Graphic plot of horizontal vs vertical (x,y) corresponds to Real numbers vs imaginary numbers.
In fractals the graphic point in Real and imaginary terms in the case of the mandelbrot is squared then added to initial (x,y) or ( Real, imaginary ) value
Z(New) = Z(old)