Do you mean... hiding the frame?

Since the frame (or the PApplet, rather) is the embodiment of the application, it is difficult to simply get rid of it. A different language might be better suited to this task. However, it is possible to hide the frame...

Try this (for me, on the first frame of draw()):

1. frame.setVisible(false);
   

It is starting to be a FAQ, people asking for Processing to be headless, on the server side, etc.
Processing isn't designed for such usage, its root is an Applet, a visual object with a life cycle specific for display.
Somehow, its code could have been organized to make little dependency on the Applet side, and around a headless core. That's partly the case around the central PGraphics, but still all functions has roots in the PApplet.

Looking closer, you can actually use PImage and PGraphics with some care (don't rely on having a default font, don't use save()) without the parent PApplet, they are quite self-sufficient, if you call their functions directly.
For lot of functions, PApplet is only a proxy passing the parameters to the default PGraphics (and other similar classes).

I just found something like this I was tinkering with when looking for something else. I'm fairly certain it will still throw some kind of exception if you run it on a truly headless setup. Add this to the start of your sketch:
{
  System.setProperty("java.awt.headless", "true");
}

and this on the same level as setup and draw (override):

boolean displayable() {
  return false;
}