x_{n+1} = x_n^2 - y_n^2 + x_0
y_{n+1} = 2 x_n y_n + y_0
(Not 100% sure I got this right, but it's late.) The Mandelbrot set is then the set of points x_0, y_0 for which these values don't escape to infinity, or even more simply, escape the circle of radius 2 around (0, 0).
Regarding the iPad, marketing-wise, they might claim that people typically hold the iPad farther away from their eyes than 12 inches, say 15 inches, which places the "retina limit" conveniently just under 260 dpi.