Greetings, I've recently came across this poster and would like to learn how the background effect was achieved, can you please suggest tips in order to start moving on.
Interesting. It is difficult to guess what is the exact process. For example, there are some programs that try to mimic particles and inclusive moving particles. For example this: http://www.escapemotions.com/experiments/fluid_painter/
I will try to do some experiments later but one option is to start in Photoshop with a simple black and white noise and start smearing it in the desired direction.
I think you can try in a low resolution and resample it later.
I would use separated layers and you can change the color of the layer and not contaminate the adjacent colors.
Another option would be trying with a painting program, like Corel Painter or the free one MyPaint, or Dogwaffle.
Note that this is not a definitive answer, but does answer:
tips in order to start moving on
One first example. This is a test on Dogwaffle Artist 9 using some particle brushes directly:
One more place to explore is using a pressure sensitive tablet.
In photoshop you can change the dynamics of any brush, sometimes the pressure changes opacity or color. In this case, you want to change size.