I'm replying again to you as I can't edit my previous reply. I forgot to mention that the iteration count in the linked site is set by default to only 200. That's the number of iterations of the formula (for the mandelbrot it's z=z*2+c where z and c are complex) is calculated to determine whether a given value of c (coordinate on the complex plane) diverges or not (the mandelbrot is the set of all values of c where it doesn't diverge. z starts at 0).

Thus you can increase the iteration count, but again more calculations.

All other things equal, more zoom leads to more precision and more iterations.