Read again the append() reference, particularly the 'cast' part.

ok, the cast part was the first to be fixed. but simply doing that isn't enough.
so i changed the way i create the new array:

1. balls3 = (Ball[]) concat(balls,balls2);
2.   for (int i = 0; i < numBalls; i++) {
3.     balls[i] = new Ball(random(width), random(height), random(20, 40), i, balls3);
4.     balls2[i] = new Ball(random(width), random(height), random(20, 40), i, balls3);
5.   }

it works half a way, because the behaviuor isn't so predictable, as you may see...
i don't understand why...

moreover, if then i try to change the color of balls and balls2, in order to better understand, in this way:

1.     cR=color(i*20+100,0,0);
2.     cB=color(0,0,i*20+100);
3.     balls[i] = new Ball(random(width), random(height), random(20, 40), cR, balls);
4.     balls2[i] = new Ball(random(width), random(height), random(20, 40), cB, balls2);

i get an ArrayOutOfBoundsException...


there's something i didn't yet understand with array, i guess

I suggest to first fix your code:

  for (int i = 0; i < numBalls; i++) {
    balls[i] = new Ball(random(width), random(height), random(20, 40), i, balls);
    balls2[i] = new Ball(random(width), random(height), random(20, 40), i, balls2);
    balls3[i] = new Ball(random(width), random(height), random(20, 40), i, balls3);
  }
  // You just erase the random balls created previously!
  arraycopy(balls, balls3);
  // It doesn't do what you think, it tries to add an element to balls3, except that an array doesn't fit here
  balls3 = (Ball[]) append(balls3, balls2);
  for (int i = 0; i < numBalls; i++) {
    // Again, you erase the previous balls!
    balls[i] = new Ball(random(width), random(height), random(20, 40), i, balls3);
    balls2[i] = new Ball(random(width), random(height), random(20, 40), i, balls3);
  }

Actually, I should question your goal... Why "create two arrays of bouncing bubbles, and make colliding the arrays each other."? (supposing arrays can collide...) OK, why not. But then, why do you create three arrays? It is confusing.

ah ah ah, sorry, arrays doesn't collide but the objects inside the array 

I know that the code is to be fixed and that I'm messing with it in a wrong way.

// It doesn't do what you think, it tries to add an element to balls3, except that an array doesn't fit here
  balls3 = (Ball[]) append(balls3, balls2);

I know, in fact i tried with ball3=concat(ball,ball2 ) too (or something similar...), and it works half a way but the two Ball Array have strange behaviour!!!


the goal is to create a composite object with a single ball rotating around a point and three bouncing ball around the screen,
I would like to create a new istance of such composite object whenever i click inside the screen.


Here's the code (without the colliding Method()):
at the moment the bouncing balls bounce just when they reach the edges of the screen...

1. UFO[] ufi = new UFO[2];
2. float[] baseX= new float[2];
3. float[] baseY= new float[2];
4. color[] rColor= new color[2];
5. color c;
6. void setup() {
7.   size(400,400);
8.   smooth();
9.   for (int i=0; i<baseX.length; i++) {
10.     baseX[i]= random(15,width-15);
11.     baseY[i]= random(15,height-15);
12.     rColor[i]= color(random(255),random(255),random(255));  
    
13.   }
14.   for (int i=0; i<ufi.length; i=i+1) {
15.     ufi[i] = new UFO(baseX[i],baseY[i],rColor[i]);
16.   }
17. }
18. void draw() {
19.   background(0);
20.   for (int i=0; i<ufi.length; i++) {
21.     ufi[i].move();
22.     ufi[i].display();
23.   }
24. }
25. void mousePressed(){
26.   float newR,newG,newB;
27.   newR=random(255);
28.   newG=random(255);
29.   newB=random(255);
30.   color newColor=color(newR,newG,newB);
31.   UFO u= new UFO(mouseX,mouseY,newColor);
32.   ufi= (UFO[]) append(ufi,u);
33. }
34. class UFO {
35.   float xBase;
36.   float yBase;
37.   float angle;
38.   float raggio;
39.   float angleInc;
40.   //fine aggiunte (per ora).
41.   float[] speedX= new float[3];
42.   float[] speedY= new float[3];
43.   float[] x_= new float[3];
44.   float[] y_= new float[3];
45.   color c;
46.   UFO(float xBase_t, float yBase_t, color c_t) {
47.     xBase=xBase_t;
48.     yBase=yBase_t;
49.     angle= atan2(yBase - height/2, xBase - width/2);
50.     raggio= dist(width/2,height/2,xBase,yBase);
51.     c=c_t;
52.     angleInc=PI/raggio;
53.     //creiamo
54.     for (int i=0; i<x_.length; i++) {
55.       x_[i]=xBase;
56.       y_[i]=yBase;
57.       speedX[i]=random(-3,3);
58.       speedY[i]=random(-3,3);
59.     }
60.   }
61.   void display() {
62.     ellipseMode(CENTER);
63.     for (int i=0; i<x_.length; i++) {
64.       //sfere dipendenti [i]
65.       smooth();
66.       stroke(120);
67.       fill(c,100);
68.       ellipse(x_[i],y_[i],30,30);
69.     }
70.     //sfera centrale
71.     noStroke();
72.     fill(255);
73.     ellipse(width/2,height/2,10,10);
74.     //linea di sfera base con centro
75.     stroke(255);
76.     line(width/2,height/2,xBase,yBase);
77.     //sfera base
78.     smooth();
79.     stroke(200);
80.     fill(c);  
    
81.     ellipse(xBase,yBase,30,30);  
    
82.   }
83.   void move() {
84.     xBase=(cos(angle)*raggio+width/2);
85.     //println("nuova xBase è " +xBase);
86.     yBase=(sin(angle)*raggio+height/2);
87.     angle+=angleInc;
88.     for (int i=0; i<x_.length; i++) {
89.       //"ponte" tra base e sfera2
90.       stroke(c,100);
91.       line(xBase,yBase,x_[i],y_[i]);
92.       x_[i]=x_[i]+speedX[i];
93.       y_[i]=y_[i]+speedY[i];
94.       //rimbalzo delle sfere reciprocamente
95.       /* for(int o=x_.length;o<0;o--) {
96.        x_[i]=x_[o];
97.        y_[i]=y_[o];*/
98.       //condizioni di rimbalzo sfera[i]
99.       if (x_[i]>width-15) {
100.         speedX[i]=random(0.2,2)*-1;
101.       }
102.       if (x_[i]<15) {
103.         speedX[i]=random(0.2,2);
104.       }
105.       if (y_[i]>height-15) {
106.         speedY[i]=random(0.1,2)*-1;
107.       }
108.       if (y_[i]<15) {
109.         speedY[i]=random(0.1,2);
110.       }
     
111.     }
112.   }
113. }