Are you using thread("myFunction") inside draw or launching it once from setup ?

Makio135
http://makio135.com/

ok, it was just to be sure.
Maybe some code could make it clearer

Have you thought about using a separate PGraphics buffer?
Anyways, Processing is not too good on threads concurrently accessing its canvas! 

Here's your sample code running 4x faster. From 80 msec to 20 msec in my slow PC! 

void setup() {
  size(480, 854, P2D);
  //size(480, 854, JAVA2D);

  background(0);
  stroke(-1);
  noLoop();

  line(0, height>>1, width, height>>1);
}

void draw() {
}

void mousePressed() {
  if (mouseY > height>>1)    doIt();
  else               thread("doIt");
}

final void doIt() {
  final int m = millis();
  loadPixels();

  for (int i = pixels.length; i != 0; 
    pixels[--i] = (color) random(0x1000000) | #000000);

  updatePixels();
  println( millis() - m );

  redraw();
}

tested this on my Samsung Note2:

@zahand: tested your last code, i get similar results with both methods (threaded or not)

Makio135
http://makio135.com/

probably, have you tested my code?

Makio135
http://makio135.com/

Tested your code, Makio135. However, screen freneticly blinked white and thread counter was very blurry! 
If I'd change engine for anything but JAVA2D, program halted quickly!

So, I've made a re-factoring of your example. And it's working alright for me now: 

PGraphics pg;
boolean isThreading;

final static String ENGINE = P2D; // JAVA2D, P2D, P3D, OPENGL
final static byte   FONT = 050;
final static short  FPS  = 0300;

void setup() {
  size(0300, 0200, ENGINE);
  frameRate(FPS);
  noSmooth();
  textSize(FONT);
  fill(#00FFFF);

  pg = createGraphics(width, height, ENGINE);

  pg.beginDraw();
  pg.noSmooth();
  pg.textSize(FONT);
  pg.fill(#FFFF00);
  pg.endDraw();

  mousePressed();
}

void draw() {
  background(0);
  text(frameCount, 010, 050);
  image(pg, 0, 0);
}

void myThread() {
  int count = 0;

  while (isThreading) {
    pg.background(0, 0);
    pg.text(++count, 010, 0150);
  }
}

void mousePressed() {
  if (isThreading = !isThreading)  thread("myThread");
}

void keyPressed() {
  mousePressed();
}

Yes, but as I said above it looks like the one in the draw loop is capped by the draw refresh rate.

It is a huge cycle:

• call draw()
• draw everything in te sketch's surface buffer
• call run()
• render current sketch's surface buffer into the actual screen
• call every extra triggered function on the queue
• decide if it still has to delay next draw() call according to frameRate()
• rinse & repeat! 

It's not just the FPS limit from frameRate(); rather, there are too many tasks to complete for each cycle!
Threaded method calls, in turn, can just draw into a surface buffer non-stop, with no other further obligation!

Perhaps, you may try to only draw into PGraphics instances instead, and let draw() the sole task to display
all of them asynchronously, w/ no regards to whether a Pgraphics surface drawing is not complete atM!

That's what I did w/ the adapted code from Makio135! The PGraphics pg buffer is continuously being drawn.
And within draw(), that layer is drawn using image() above the main sketch surface,
no matter whether pg has a full refresh state!

@GoToLoop: tested your code and got the following error:


Makio135
http://makio135.com/

I still use current stable Processing v1.5.1! 
In this version, engines P2D & P3D are "real"! Beta versions axed them out and use OPENGL instead! 
That's why I've set a constant to change the graphics engine used -> ENGINE
Just use instead:

final static String ENGINE = JAVA2D;

P.S.: I use P2D b/c it's über fast!