last frame of particle animation to become part of the background image

hi

I want the last frame of a particle animation to become part of the background image.

Being able to do this would give the ability to have an infinitely evolving background image, without the system falling over.

What would be the best way to achieve this?

thanks

Matt

or it could be an instance of an animated object (instead of a particle), the final frame of which is “baked” into the background image as the object removes itself from the scene.

?