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How can I get two particle systems to attract particles from their same system and repel particles from the other system?
I tried using charge and a negative field weight for charge, but that just causes the force to cease.
Step 1: Kys

Nah in all seriousness tho, I'm assuming you are using blender, you can use boids particles and mess around with their settings. I don't know much, but try this tutorial

I'd prefer not to use boids, this is just to test a physics concept.
How easy would it be to modify Blender by myself to make a new particle forcefield that's like charge but with reversed effect?
This might help:

Why would that help?
I already know what every forcefield type does.
make first particle at o,o,o assign it features u need
My problem is that I can't assign the features I need.
Why bother doing this in blender (or any other software)? Just program it yourself.

I can link you some code for a galactic cluster simulator I've written a while ago that shows the particles as glowing dots (with some optional trails)
Blender's a very nice engine for doing it, it seems easier to tweak it a little than to write something from scratch.
What do you hope to gain from using it? A prettier render result?

If you want to test a physics concept, you'll want to write the integrator yourself anyway...

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