First I checked to see if the difference between the current size of the particle and the desired size was greater than 1. If this was true, then the difference in size would be cut in half, yielding a size closer to the desirable.
Then, using the distance formula I found the distance between the current (x, y) position of the particle and the (x, y) position of the destination. If there were still some distance to move, then we'd want to move closer to the destination. So if the distance is greater than 1 pixel, the goal has not been met. The (randomX-this._x) and (randomY-this._y) statements will give us the distance needed to move (it could be positive or negative, depending on position). Now, the easeFactor variable will affect this highly. With a low value, the particle will move over to its' destination extremely fast (the distance between the two points will be cut in half every time, if the easeFactor were 2). With a larger easeFactor, the distance the particle will travel will be cut down even more. I chose 10 because I like the way it looks, but it's all a matter of opinion.
At the end of the move sequence, the movie will "recycle" itself, so to speak, and go back to frame 2. It will repeat this process until the distance is less than one, in which case it will return back to frame 1 and pick a new point to go to.
For the sake of simplicity, I made particle duplication rather easy. All I did was place a bunch of instances of the movie in the main frame of the flash file. So exit out of symbol-editing mode, back to the main screen, then drag and drop a bunch of particles everywhere. Make sure you are placing instances of the particle movie, and not just the graphic. Then test the movie, the end result should look like this: