The following is a demonstration of using MEL scripting to create randomized curves in a shape of spirals as a particle path. Using a single emitter at the origin, particles flow through the spirals in a helix pattern. As particle ages, they become larger and more saturated.
Video above examines the form of three types of particle densities.
Particles Along "Random" Curves
Sets of curves are randomized by each creation for unique shapes. Each spiral curve is then offset from one another.
Particle Density Levels
Density Level: 1
Density Level: 2
Density Level: 3