It really depends on the fractal, and there are many possible ways to define them. As an example, for the Mandelbrot set, a number of calculations involving complex numbers are done for each point in the complex plane, to determine whether a point is part of the set or not. However, other definitions are possible as well.
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Pi is a number. There are no fractals of pi.
No. Fractals are geometric shapes which include high calculations. I'm not even able to do the first part of it.
If you look closely and carefully enough, nature is ALL fractals; snowflakes, leaves, tree branches, coastlines, everywhere.
Benoit Mandelbrot
Fractals are commonly used for digitally modeling irregular patterns and structures in nature. They are also very useful for image compression, producing an enlarged picture with no pixilation.