Animating dots as if they were a crowd of people

Do you have access to the individual dots as layers? If so, you could apply some random motion that resolves to the inital position of the dots with a position expression set up like this:

minResolve = 3;
maxResolve = 5;
maxAmp = 200;
seedRandom (index,true);
resolve = random(minResolve,maxResolve);
amp = linear(time,inPoint,inPoint+resolve,maxAmp,0);
wiggle(.5,amp,4)

If you use the Shatter Effect.

You can set a custom pattern, use the graphic layer itself.

And you can flatten out the layer turnign off extrusion depth.

And you can remore 3d rotation in the Physics group.

I use this alot with shape  layers, I've never tried it with a graphics like the one in your example though.

You can easily make everything look 2D, but of course it will take some massaging of the parameters. It would probably be best to provide screenshots of your current settings so we can advise on what to tweak.

Mylenium 

The typical approch is to explode the logo, then time-reverse the animation. A logo like yours based on a regular grid can easily be "exploded" using Card Dance, Shatter, CC Ball Action or even good old Particle Playground. It will just take time to understand how these effects work plus of course you may need extra fiddling to get the illusion of dots actually "walking" in a natural fashion rather than moving in straight direct lines to their position, which may still necessitate lots of hand keyframing in addition to relying on the automated effects. I suggest you research "exploding logo" or "text to sand" types of tutorials on YouTube and elsewhere.

Mylenium