Script to move playhead randomly to frames?

Yes, you just need to have a random number generator paired with a gotoAndStop() call as part of a setInterval() scenario.

var intervalID = setInterval(moveToFrame, 8000);

function moveToFrame(){

     gotoAndStop(Math.ceil(Math.random()*20));

}

Actually, I forgot that the random function could return a true zero value, which would get you nowhere, so here's an alternate:

var intervalID = setInterval(moveToFrame, 8000);

function moveToFrame(){

     gotoAndStop(Math.floor(Math.random()*20)+1);

}

You should get familiar with the Math.random() function... hon'st.  It's the primary tool used when you want to randomize things, whether it's frame numbers or _x/_y positions or _alpha values or whatever else can be defined by some kind of range of values.

Please mark this posting as answered if you still can.

Think about what you want the screen saver to do--I can't determine that for you.  If you understand what you can use Math.random() for, then you really should be able to move on and do whatever random thing you are trying to.  If you can understand what you want of it, then there is no reason you can't try to create it... just pursue it one step at a time.  You'll be much happier with your solution if it's something you created yourself.

As far as showing the same thing in a row too often, the chances are pretty high that will happen when you only have 4 frames (25% chance... fairly high probability).

As for the time getting shorter, it is most likely because you return to frame 1 every so often and create another interval, so you end up with more than one firing.  You need to disallow that code from executing for any return trips to frame 1.

I didn't say to code it so you don't return to frame 1, code it so that when you do return to frame 1 you don't initiate another setInterval... you only want one working.  If you put the following code in frame 1 it will take care of that, only allowing one setInterval to be activated...

stop();

var intervalID; // intervalID is undefined here because it has nothing assigned to it

if(!intervalID){ // will only process when intervalID is undefined
  intervalID = setInterval(moveToFrame, 3000); // defines intervalID
}

function moveToFrame(){
     gotoAndStop(Math.floor(Math.random()*4)+1);
}