Per-Particle Radial Fields

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Create a particle system, select it, and create a Radial Field

Select both the Radial field and Particle System and execute “Use Selected as Source of Field”. This causes the particle system itself to exert the Radial Field.

Open the Attribute Editor for the Radial Field and select “Apply Per Vertex” under the “Special Effects” tab. “Apply Per Vertex” will  cause a Radial Fieldto be created per particle, so that each particle can affect those nearby.

These are the attributes you'll probably want to change to tweak the affect of the Radial Field.

Here are some example defaults. Attenuation of 0 will mean that the Radial Field has the same affect everywhere within its region of affect (as determined by Max Distance). This is a close approximation of rigid body collisions.