In the draw() function, the background color is used to clear the display window at the beginning of each frame.

If you wish to change the color of the background without clearing the screen, I believe the best way to do so is to create a rectangle the size of the screen size and to draw it on a negative layer. By default, everything is drawn on layer "0" so if you draw a rectangle on layer "-1", whatever is drawn on top won't be erased. To do so, you need to be either in P3D or OPENGL.


The example below changes the background from black to white, and when the color reaches 255, right back to black. It's up to you to change the variable in the fill() to reflect the color you want. It draws red squares randomly to show you that nothing gets erased.

Code:

int bgColor = 0;

void setup() {
  size(800,800, P3D);
  background(0);
}

void draw() {
  pushMatrix();
     translate(0,0,-1);
     fill(bgColor %255);
     rect(0,0,width,height);
  popMatrix();
  
  bgColor +=5;

  fill(255,0,0);
  rect(int(random(width)), int(random(height)), 10,10);
}
 

Hope it helps!