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This animation is of the entirety of the Mandelbrot set, as the number of iterations calculated increases. As the number of iterations is raised, the "black" colored area hugs the true Mandelbrot set more tightly. The function that drives the Mandelbrot set is an iterative function with no end, so no number of iterations will show the set completely. Practically, though, once you iterate enough at a certain zoom level, there's no discernible difference that comes from iterating further.

This animation is of a zoomed-in area of the Mandelbrot set, showing the effect that increasing the number of iterations has on a zoomed in area.