Perturbulance is an noise function, where you give a position and a distance from this point. It will then calculate a pseudo-Random point with in the distance. The nice thing about this in relation to island creation is ,that an island is an central point where the further you go the lower it gets. This generates a basic island where the terrain is high in the middle and low ad the endges. Then using some noise functions to generate some more terrain like features gives an pretty decent start for the island.

The sea is still to rough to be a real island and on some point a bit to deep. So the next thing that is needed is checking which point go lower that the lowest low and change their height. To smooth out the underwater terrain we'll add some hydrolic errosion.