The initial click on Action shows the biundary of the Mandelbrot set. After clicking Action, click the mouse button at a point on the screen where you want to start an iteration trail. Then click on Action to iterate z2+c. If the trail leads out of bounds, the Action button becomes disabled.
In iterating the function you may have observed that points close together tend to produce similar patterns of x's. Some were blobs, some were simple inward spirals, some were compound inward spirals, that is spirals with multiple branches, some were closed loops and so on. The complex ways in which z2+c converges for points inside the set is mirrored by the ways in which those points immediately outside the set produce divergence. The number of iterations it takes to diverge varies greatly depending on the starting location.