Points in the Mandelbrot set

Off[General::spell];

Off[General::spell1];

c = ; (* paste the c-value here. For example, c = -.4 + .5*I *)

iters = ; (* number of iterations - start small, say 5, until you're sure the c-value you picked belngs to the Mandelbrot set. *)

z = 0;

f[z_] := z^2 + c

pointlist = {};

Do[{z = f[z], Print[z], AppendTo[pointlist, Point[{Re[z], Im[z]}]]}, {i, 1, iters}]

Show[Graphics[{PointSize[ 0.05], pointlist}], AspectRatio -> Automatic, Axes -> True]

(* Be careful. The plotted axes need not meet at the origin *)