That's absolutely right, but it's not the only reason. The interesting bits of a Mandelbrot set plot are the ones that are on the boundary of the set itself. Re

That's absolutely right, but it's not the only reason. The interesting bits of a Mandelbrot set plot are the ones that are on the boundary of the set itself. Remember that the Mandelbrot set is the set of points for which a particular iteration never diverges to infinity. So a point outside the set but very very close will diverge very very slowly: it will take a lot of iterations before you can tell it's outside the set. (The colours you see in a typical Mandelbrot set plot indicate how many iterations it takes.) So, if you zoom really close in then every point in your plot either lies outside the set but takes many iterations to determine that, or lies inside the set (and therefore takes as many iterations as you're prepared to do). So you're doing more iterations, with higher-precision numbers, as you zoom closer in.