I'm going to be away for a while so I only have time for a quick sample project. Hope it helps:
https://www.dropbox.com/scl/fi/eh15f17mkrr2nzq91307e/lazy-flame-01A.c4d?rlkey=ktkcf6drnefb28pw52g1zuh9f&dl=0

That does sound odd. I think you may need to contact customer support and report this. Maybe it happens on some configurations.

You discovered a bug in the "Compactify Threshold" Setting in the Simulation Settings - Particles.
Set the Compactify Threshold to 100% and it will work...

EDIT: Maxon is already aware and is working to fix this.

@danphish Requested access

You need to simplify the scene and only leave the necessary elements, and upload somewhere I can download it from ...

You're doing nothing wrong as far as I can see... this appears to be a glitch on your system right now.
Do the usual, restart C4D, Restart PC, remove Preferences, reinstall C4D in a new Folder.

One at a time

I just used it in 2026.3.4 and it works fine. Changed Mirror Plane and Coordinate system and it just works as expected.
Can you elaborate a bit more?

What is the "Chance" Percentage in your Condition?

Unfortunately this doesn't appear to be a trivial problem to solve. I could dive into it more but this requires some algorithm rather than a "clever" setup. I spent some time to prompt an AI agent to do it in html - JavaScript and while it appears to work, the results are not nice, proving this is not a simple case of just adding random tiles and then filling the gaps... I will do some more research because it's an interesting topic but have no idea if something will come out of this...
Here's the link to the AI code. Change the Seed for a different layout.
https://www.noseman.org/school/experiments/tiles01.html

There are two parts in your request.
One part is the execution of this setup, but the most important part is the logic. How would the tiles fit next to each other?
You need to be able to explain how that logic would work by making some sample manual setups and writing an overview of what you want it to do.
If you provide a scene file with some examples and write an explanation of the logic, I will give it a show and maybe make a tutorial.

@Lnrd_ said

...I need to be able to rotate the independent geometries while keeping the IK.

I'm not sure I understand that.

Have you watched this tutorial?
https://cineversity.maxon.net/en/tutorials/kinematic-limits-how-to-rig-robots

so, this was harder than I thought... maybe there's a simpler way but I need tome to think about it.

The general idea is to cache the RBDs (balloons) and the particles to separate Alembic files, use the particle alembic ONLY ON FRAME 1 to clone the Splines and make them Ropes and add a Connector Tag, NOT a Rope Belt.
Put the Balloon Alembics into a Connect Object and make it a cloth with Mix Animation 100%.
Make the Rope Spline Connector Tag search until the ropes find the Balloons.

Here's the final file and the RBD alembic:
https://www.dropbox.com/scl/fi/hug88hs5ubq3rwdqa2m0b/balloons-final-with-Strings-01A.c4d?rlkey=5274a024islzj8sc7smkmrukg&dl=0

https://www.dropbox.com/scl/fi/7x7y1dk862azezkskbl72/balloons-final_Rigid-Body_v0.abc?rlkey=za6mv95rnkosv9zxxpyqu18bv&dl=0

requested access for your project file...

here's the latest build:
https://www.dropbox.com/scl/fi/psnk4v0ng5ukhsfpplkxg/Py-ParametricTools.zip?rlkey=loi7f8x2x5ldljwmfqy4e6s1h&dl=0

can you please create a very simple scene 3-4 balloons (Spheres) and show me what you're trying to do and show me "The strings weren‘t behaving properly within the cloner"...
thanks

@cookie-assignment
Please report these to Customer Support.

You can use a Spline with 16x9 size as a child of your camera. Just move it slightly in front of the camera
https://www.dropbox.com/scl/fi/w1p5amtw305bhu4onyyud/Camera-Guide-16-9.c4d?rlkey=uli89elde1h3o5geob5bswfsy&st=1uwr1m13&dl=0

You can post a link to the file and also I need to know how you want to animate it.
"the rotations be free"... I don't know what that means.

Also watch this:
https://cineversity.maxon.net/en/tutorials/kinematic-limits-how-to-rig-robots

Which tutorial did you follow that shows a Protection Tag?
Here's another way using Math. No need for Protection Tags:
https://www.youtube.com/watch?v=s4fVHewn_IU