Hi,
I got your program to learn and practice control with the mouse.
I might send you a modified version of it later.

The circles you draw follow the mouse.
What do you mean by <allow it to jump randomly> ?

I'm sending you the code I have right now:

////////////////////////////////////////////////////
static int nRGB = 256;

void setup()  
{
 size(600, 600);
 background(185,216,255);
 color(57,114,185);
 noStroke();
 ellipseMode(CENTER_RADIUS);

}

void draw()

{
 //// draw an egg with mouse-changing color
 fill(96);
 arc(150, 50, 50, 100, 0, PI/2);
 fill((mouseX*nRGB)/width,144,(mouseY*nRGB)/height);
 arc(150, 50, 150, 100, PI/2, PI);
 fill(160);
 arc(150, 50, 150, 50, PI, TWO_PI-PI/2);
 fill((mouseY*nRGB)/height,208,(mouseX*nRGB)/width);
 arc(150, 50, 50, 50, TWO_PI-PI/2, TWO_PI);
 fill(255);

 if(mousePressed==true)
 {
   noStroke();
   wheel a = new wheel();
   a.draw();  
 }
 else
 {
   rotellipse e = new rotellipse();
   e.ellipsechange(mouseX, mouseY, pmouseX, pmouseY);
 }

 // black rectangle covers images
 if(keyPressed)
 {
   if(key==' ')
   {
     background(0);
   }
 }    
}

// draws ellipses
class wheel
{
 int wheels = 50;  
 float xpos[] = new float[wheels];  
 float ypos[] = new float[wheels];  
 float b = random(100);

 void draw()
 {  
   xpos[wheels-20] = mouseX;  
   ypos[wheels-20] = mouseY;  

   for(int i=0; i<wheels; i++)  
   {  
     // ARCS HERE
     stroke(128);
     int xx=int(random(width));
     int yy=int(random(height));
     int rx=int(random(10,width/6));
     int ry=int(random(10,height/6));
     arc(xx, yy, rx, ry, 0, PI/2);
     arc(xx, yy, rx, ry, PI/2, PI);
     arc(xx, yy, rx, ry, PI, TWO_PI-PI/2);
     arc(xx, yy, rx, ry, TWO_PI-PI/2, TWO_PI);
   }
 }
}    

// draws ellipses randomly
class rotellipse
{
 float move;
 void ellipsechange(int x, int y, int px, int py)  
 {  
   smooth();  
   move = abs(x-px) + abs(y-py);  
   translate(mouseX, mouseY);

   stroke(10, 0, 10/2);
   ellipse(5,5,5+move,5+move);  
 }
}