Without even looking at your code, this sounds like a classic problem; you're working under the assumption that anything in draw() is drawn automatically. Instead, however, the canvas is only updated at the end; you are effectively displaying only the last position.

You have to split it up across several frames (probably with an incremental variable)...

See I display several images in sequence, but I only see the last one. Why? on the Processing Wiki.

Thanks calsign !

here is another approach using lerp....

1. // /*    Circle moving between two points chosen among a set of random ones  */
2. PImage monImage;
3. final int imageWidth = 100;
4. final int imageHeight = 100;
5. final int displayWidth = 500;
6. final int displayHeight = 500;
7. color myColor;
8. PVector startPoint = new PVector() ;
9. PVector endPoint = new PVector() ;
10. PVector currentPoint = new PVector();
11. final float numSteps = 100.0 ;
12. ArrayList possiblePoints = new ArrayList();
13. int currentTime;
14. float i=0;
15. void setup() {
16.   size(displayWidth, displayHeight);
17.   monImage = createImage(imageWidth, imageHeight, RGB);
18.   // random filling of image
19.   for (int i = 0; i < imageWidth; i++) {
20.     for (int j = 0; j < imageHeight; j++) {
21.       // creates random points and stores them
22.       int test = int(int(random(1000)) >= 999);
23.       if (test == 1) {
24.         myColor = color(255, 0, 0);
25.         possiblePoints.add(new PVector(i, j));
26.       }
27.       else {
28.         myColor = color(255, 255, 255) ;
29.       }
30.       monImage.pixels[(j*imageWidth)+i] = myColor;
31.     }
32.   }
33.   shapeMode(CENTER);
34.   fill(255, 255, 255, 127);
35.   stroke(0, 0, 0, 255);
36.   monImage.updatePixels();
37.   //frameRate(17);
38.   // displacement
39.   // choice of two random points within the ones generated in setup
40.   startPoint = (PVector) possiblePoints.get((int(random(possiblePoints.size()))));
41.   endPoint = (PVector) possiblePoints.get((int(random(possiblePoints.size()))));
42. }
43. void draw() {
44.   background(255);
45.   image(monImage, 0, 0, displayWidth, displayHeight);
46.   currentPoint.x = lerp(startPoint.x, endPoint.x, i / 100.0 ) ;
47.   currentPoint.y = lerp(startPoint.y, endPoint.y, i / 100.0 ) ;
48.   ellipse(currentPoint.x, currentPoint.y, 10, 10);
49.   i++;
50.   if (i>=numSteps) {
51.     i=0;
52.     // displacement
53.     // choice of two random points within the ones generated in setup
54.     startPoint = (PVector) possiblePoints.get((int(random(possiblePoints.size()))));
55.     endPoint = (PVector) possiblePoints.get((int(random(possiblePoints.size()))));
56.     if (startPoint.dist(endPoint)==0) {
57.       println("Same points  :-(   ");
58.     }
59.   }
60. }

Very interesting Chrisir ! Thanks a lot !