###This is most certainly not easily done in blender. 

Check out flame painter: http://www.escapemotions.com/products/flamepainter/

However, similar things have been done in blender https://blender.stackexchange.com/questions/7434/abstract-wave-with-particle-system

It is much much easier not to use blender for this task. In fact, I even have a demo of something similar to this that runs in realtime in JS http://codepen.io/Thisisntme/full/KNpPEz/
[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/Wnuhm.png

If you wanted to know, my codepen works by creating a sequence of lines, and then dragging them down the screen (from left to right although it doesn't really matter) all while changing the y position with a few trig functions.