You can do it like this. The next step would be to replace all the 'magic numbers' by variables. Then it really becomes fast and easy to adapt to different situations.

Code Example

1. void setup() {
2.   size(400, 400);
3. }
4.  
5. void draw() {
6.   for (int y=0; y<4; y++) {
7.     for (int x=0; x<4; x++) {
8.       pushMatrix();
9.       translate(x*100, y*100);
10.       rect(0, 0, 100, 100);
11.       if ((x+y) % 2 == 0) {
12.         line(0, 50, 100, 50);
13.         line(50, 0, 50, 100);
14.         rect(25, 25, 50, 50);
15.       } else {
16.         line(33, 0, 33, 100);
17.         line(66, 0, 66, 100);
18.       }
19.       popMatrix();
20.     }
21.   }
22. }

This is what it would look like with parameters. Now you could change the dimensions or the gridSize and it is flexible. The only assumption is that the sketch dimensions are square as well. Try setting dim to 1000 and gridSize to 24 for example. You will see that the computer will work it out automatically.

1. int dim = 400;
   
2. float gridSize = 4;
3. float full, quarter, half, third;
4.  
5. void setup() {
6.   size(dim, dim);
7.   full = width/gridSize;
8.   half = full/2;
9.   quarter = full/4;
10.   third = full/3;
11. }
12.  
13. void draw() {
14.   for (int y=0; y<gridSize; y++) {
15.     for (int x=0; x<gridSize; x++) {
16.       pushMatrix();
17.       translate(x*full, y*full);
18.       rect(0, 0, full, full);
19.       if ((x+y) % 2 == 0) {
20.         line(0, half, full, half);
21.         line(half, 0, half, full);
22.         rect(quarter, quarter, half, half);
23.       } else {
24.         line(third, 0, third, full);
25.         line(2*third, 0, 2*third, full);
26.       }
27.       popMatrix();
28.     }
29.   }
30. }