Trail particles ending in a point? I'm back with another question.

I've been working on a particle system, and I have a cube which outputs square particles from its volume without a normal movement value, then, I move the cube around (via keyframing).

My only problem is that particles usually achieve something similar to the right side of this image:



When what I really want to achieve is what's on the left.

Is there any way I could move the particles to form a point at the end?
You could emit objects from a vertex group of a ico sphere. Let the emitter follow a curve a force field could follow the emitter and attract all particles. The distance of the force field can be controlled by offset.



The fade out of the trail can be controlled by the particles age e.g.



(Note that the particle count has been lowered in the .blend) The age is not correctly calculated when using child particles.