Make 4 or 16 or etc. smaller images. Assemble them with an image program (Gimp, Photoshop, ImageMagick...), perhaps after reducing their color depth (if possible) to reduce overall size.
Should work well given the kind of image you create...

I did the same math... and had no answer!

But perhaps you create lot of objects for your variations on images, saturating the memory before the garbage collector kicks in.

I don't think I create a lot of objets in the memory because  I just use  one image (500x500 pixel) as a stamp...
I already use createGraphics() and I render it offscreen without displaying it...

this is the code I'm using actually....




String gStampImageName="p2";  
String gArtworkName= "BigImage";  // this image will be saved in png
int gBigImageSize = 4000; // here I would like to have 12000
float gStampSize=80; // same scale as the displaysize


Stamp gDrawingStamp;
PImage gSourceimage;
int gDisplaySize=1000;// size of the preview
int gBackgroundColor=0;
float gStampRapportSize;
PGraphics gBigImage = createGraphics(gBigImageSize, gBigImageSize, JAVA2D);
Boolean gFiniFlag=false;
int gCounter=0;
int gUpdateFrameCounter=0;
int gUpdateFrameNbr=100;  // we have a preview every 100 stamps
float gStartTime;


void setup()
{
 size(gDisplaySize,gDisplaySize);
 background(gBackgroundColor);
 smooth();
 gStampRapportSize=gBigImageSize/gDisplaySize;  

 gDrawingStamp=new Stamp(gStampImageName,113,606,0,0);  // 4 values x1,y1,x2,y2 for the regpoint and the orientation


 gStartTime= millis();
 gBigImage.beginDraw();
 gBigImage.background(gBackgroundColor);
 gBigImage.smooth();
}

void draw() {
 while (gUpdateFrameCounter<gUpdateFrameNbr) {
   gCounter++;
   gUpdateFrameCounter++;
   float r= gCounter*.5;
   float angle= gCounter*.5;
   gDrawingStamp.Show(gDisplaySize/2+r*cos(angle) ,gDisplaySize/2.0+r*sin(angle),angle,random(255), random(255), random(255), gStampSize);
  }

 gBigImage.endDraw();
 image(gBigImage, 0, 0,gDisplaySize,gDisplaySize);
 gBigImage.beginDraw();
 if (gCounter>=1000) {
   gFiniFlag=true;    
 }
 else{
   gUpdateFrameCounter=0;
 }

 if (gFiniFlag) {
   gBigImage.endDraw();
   float t=millis() - gStartTime;
   println(" Computing Time = " + t );
   gStartTime=millis();
   gBigImage.save( gArtworkName +".png");
   t=millis() - gStartTime;
   println(" Save Time = " + t );
   noLoop();
 }
}

class Stamp {  
 String  myStampName;
 int myStartX;
 int myStartY;
 int myEndX;
 int myEndY;
 float myDirection;
 PImage myStampImage;
 float myStampRealSize;

 Stamp(String Name, int sx,int sy,int ex,int ey) {
   myStampName=Name;
   myStartX = sx;
   myStartY = sy;
   myEndX=ex;
   myEndY=ey;
   myDirection = atan2(ey-sy, ex-sx);
   myStampRealSize=Distance( sx, sy, ex,ey);
   myStampImage = loadImage( myStampName + ".png");

 }

 void Show( float theX,float theY,float theAngle,float theRed,float theGreen,float theBlue,float theStampSize) {
   float MySize= gStampRapportSize*theStampSize/myStampRealSize;
   gBigImage.translate(theX*gStampRapportSize,theY*gStampRapportSize);
   gBigImage.rotate(theAngle+ myDirection);
   gBigImage.tint(theRed,theGreen,theBlue);
   gBigImage.image(myStampImage, -myStartX*MySize,-myStartY*MySize,myStampImage.width*MySize,myStampImage.height*
MySize);
   gBigImage.rotate(-theAngle- myDirection);
   gBigImage.translate(-theX*gStampRapportSize,-theY*gStampRapportSize);
 }
}

float Distance (float x1,float y1,float x2,float y2) {
 return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}