How can I use layer axis versus world axis to animate?

Question

Hi all,
I'm open to alternate ways to approach this.
I'm trying to create a sphere using several images. Say, 200 images, arranged in 3d space so they face outwards and are all forming one large sphere. Pretty standard thing (like the glowing blue droid apps sphere in the android commercials, like this).
I used Red Giants PlaneSpace to quickly make a sphere. I wish to 'explode' the sphere so all pictures move away from the spheres center, but in a staggered and random way rather than all at once.
I thought this would be easier as I see each layers orientation changed each layers axis. Thus the the layers Z-axis points away from the center.
Example:
I tried using a simple linear expression to update the Z axis over 20 seconds to its current position minus 2000, like this:
amt=linear(time, index, index+20, position[2], position[2] - 2000);
transform.position = [position[0],position[1],amt];
This updates the Z-axis position but it's based on the world axis (or comp axis), not the layers axis. The layer axis I refer to is the axis widget that appears when you select a 3d layer and the red/green/blue 3-way axis widget appears.
How can I get the expression to use the layers axis rather than world?
Is there another approach to this? I'm definitely not up to date on 3d trig enough to write a formula to plot a course away from a specific 3d point. Hopefully there's a simple way to do it that I overlooked.
I will add that I did tie all of the 200 pictures to a null, scaled the null and it does push all the pictures away. I also added an inverse scale expression so they stay the same size as they originally were instead of scaling up with the null. However I really want to make them explode in a random fashion rather than "all at once" and I need to get away from the null scaling concept for that to have access to each individual picture.
Thanks!

Answer 1

Thanks for that info!
This is a little off original topic but on the same mission: I'm trying to get them to start at random times. I think it comes down to my lack of understanding on 'when' expressions are calculated. I tried to supply a random() value to linear() but it seems every single frame these things are recalculating.
Is there a way I can generate a random number once and not every single frame so I can have each picture start at a random time?
I was trying to the effect of: linear(time,random(0,10),20,0,-2000); but that just seems to re-randomize every frame so expressions must be calculating more than once, or once per frame.
If I supply linear with static values (e.g. linear(time,0,10,0,100)) it works and will give me movement starting from second 0 moving to the value 100 over 10 seconds. If I wanted to start from a random second but always take 10 seconds, how would that work in the expression?
The idea is to get the pictures to explode in a bit of a random order which means some come before others. Maybe seeding is my issue?