###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 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/