Droste in CC - possible no-plugin solution with caveats
I was looking to do a Droste effect in CC, and was disheartened to see that the best solution is no longer an option without spending money, and then I had a bit of a flash this morning, and figured out a way to get the basic effect in CC without plugins.
Get your clock image, for instance (practice on a clock - other ideas would have to take a lot of pre-planning, and this approach is probably best understood with the classic clock motif), mask its outside and inside, so the shape of the image is a donut. Add a rotate expression here, if you wish, for some extra movement within your finished comp - time*30 will have the numbers spiraling out, time*(-30) will have them spiraling in. Pre-compose to a new composition.
Animate your clock comp scale 0 to whenever its inner mask is outside the screen area - on the slow side is better for this hack to work smoothly (mine grow from nothing to out-of-frame in 15 seconds. Even slower will make things even easier). Keyframes, I think, should be Exponential Scale, though your mileage may vary. Precomp Again.
Take your Scaled Comp and duplicate it over and over, shifting the individual timelines by the same amount (in my case, it was 40 frames) you have lots of growing clock images within growing clock images. PRE-COMP this, and put it into your main composition.
NEW BLACK SOLID. Following effects: RAMP - white to black, left to right, edge to edge. POLAR COORDINATES - rec to sphere, so you end up with a radial gradient, black around to white. LEVELS - so you can adjust things later. Scale up so that the radial ramp covers the entire area of the comp. PRECOMP.
You should now have TWO layers, total, on your main comp - the multiple growing clock comp, and the gradient ramp comp.
The next couple of steps are in your main comp.
On your MULTIPLE SCALED CLOCKS Pre-comp, drop in TIME DISPLACE, with your Radial Gradient Precomp as your map layer.
Adjust your time displacement amount until everything lines up from one clock to the clock behind it. It takes a bit of messing about - there's no hundredths adjustment in time displacement, so you'll be lucky if it's "perfect". So, if everything ALMOST lines up, you can use the levels adjustment within your gradient precomp to adjust the timing to a finer level (the bottom graph which determines the limits of your levels - for instance, moving the left arrow changes your blacks slowly to grays - play with it, you'll see the effect it has live-ish if you lock the display to the main comp as you make the adjustments on your gradient precomp). I everything is set up correctly, you'll have a nice growing spiral of never-ending clock faces, the numbers of which will move along the growing spiral (or against it) at the speed you set in your original Clock comp. The greater your time resolution, the smoother your scaling will be.
The only real limitations I've found to this approach are as follows - you have to pre-plan your movement and can't really mess with it too much or it breaks; you have to be precise in your positioning of elements in time. There is also a tiny hazy line where the time displacement breaks down right at the border of white and black. I found that rotating the gradient comp in sync with the spinning clock comp minimizes this a bit, and at least makes it such that you can apply some masked fixes over the top. Of course, there might be a more elegant answer to that particular conundrum.
Sorry if this has already been dealt with - I was just so excited to figure this out (I've only been working in AE for a month)!