I can say what I would do:
1. prepare a layer with some kind of opacity scale animation of that circle
2. Duplicate that layer as many times as I have to
3. Relocate those dots/circles on places where they should be
4. move those circles in time - f. eg. if my animation on circle is 1sec (24frames) - move each circle's start time for 5-10 frames (depends on what the final effect is best for you). For that kind of layer start movement you can use Sequence Layers in AE or some script that can do that for you.
You can also check that script - maby that will help: Locations - aescripts + aeplugins - aescripts.com
There's a few ways I can think of but it depends on what software you're using and how much control over where the circles appear you need. If you need very precise control over where the circles appear then you probably need to do it by hand and you should probably pre render it once it's set up.
You can make a single animated circle on a layer and map it to a particle grid.
If you know nothing about using particles in AE then the you spend trying to do
it with particles might take as long or longer than doing it by hand but in the end you'll have learned
something that WILL save you time the next time you need it.
Depending on your AE version you may have any or all of
Particle Playground, Particle World or Particle Systems 2
Look under your simulation effects to see what you have then check the help or Youtube to learn how to use it.
Other options are Trapcode Particular or Trapcode Form which are powerful 3rd party plugins that cost money.
If you have recent version of AE with Cineware then C4D mograph tools might also be an option although being
you didn't think of that already I'd guess you don't use it very often if at all and the learning curve would probably not be worth your time (unless you've got plenty of it)
Do a google search for something like "using particle effects in AE" or "Instancing animation in AE" or "Creating swarms in AE"
The Truth Is Out There!!
Thanks so much, yes, that's the way I would as well, but... but.... gaaaaaaaaa... time consuming!!!! Hoping for an introduction to some language of magic formulas...
Thanks so much! Yes, these are the hints I was hoping for. I don't have a whole mess of time, but recently learned of Chinaware being under the hood, and will look into all your other suggestions as well! Many thanks to both of you!
I would create a small comp that was as big as the biggest circle you wanted to animate then animate a shape layer so the circle expanded. Maybe a repeater too. If you wanted each circle to be a different color I would make the circle 50% gray and add the color later. If you wanted the circles to continue to expand or make a bulls eye and then freeze I would use the repeater function. When you get the animation working the way you want it to work you now have two options. You can use a particle system like Particular and use this small circle comp as a particle or if you wanted to have the circles start in major population groups first and then build you could add your circle comp to your main comp and then duplicate it a bunch of times, drag them to the right position. To spread out the start times you could add time remapping to the first nested comp, go to the last time remapping keyframe then move back one frame and add a new keyframe, then delete the last keyframe. This will hold the last frame and let you extend the out point of the layer to any length. If you want to have the expanding circle repeat enable time remapping, follow the same steps, and add a loopOut(); expression.
You could then duplicate the comp for as many instances as you would like and use the Keyframe Assistant to sequence the layers and overlap them. This mixed with Particular could quickly fill your map with hundreds or thousands of animated circles.
If you wanted different colors or changing colors you could also add an expression based on the index of the layer or whether the layer was a multiple of some number like every 3rd layer would be green. You would use tint, hue saturation or fill for that. In particular you can also animate the color fill of particles.
Another option would be to create a shape layer with a single animated circle then use an expression to randomize the position of the layer and duplicate it as many times as you like. If your comp was 1920 X 1080 you would add his random expression to the Transform Ellipse 1>Position property:
x = random(-900, 900);
y = random(-450, 450);
Using the layers index (number) as a seed and setting timeless to true means the layer will stay in position. Setting the max and minimum values chosen here keeps the circles inside an area 1800 X 900 pixels because shape position is at 0,0 which lines the shape up with the layer's anchor point and centers it in the window.