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
On
(I gave the answer above as well) Given the lack of answers to your question I'll link you to this. It should give you more than you can handle, which is why I refrained, I barely understand it myself, but hey maybe I'm projecting. It'll answer all of your questions.
You need to calculate a lot of points and find which points stay finite and distinguish points that take a long time to go to infinity from points that take a short time. Basically use a computer, then look at the result. Also its a fractal, so the boundary can't be determined, it would have infinite points in it. You could approximate it however, use different colors for different escape times.