How does one determine the containing boundary of a fractal?

In the Mandelbrot set, the fractal is said to be contained in the circle of radius 2. $$z_{n+1} = {z_{n}}^{2} + c$$ I did read about a proof that showed values of 'c' beyond this circle are not bounded and hence the set is contained within.

But say if someone discovers a new set that generates a fractal, How does one determine the containing boundary of that fractal ?

PS: I have studied basic engineering Mathematics and learning fractals on my own