Just a quick test to make fancy images out of b/w triangles. I fully agree on the lack of mathematical elegance. Maybe I'll clean this up sometime. Or then not.

gistfile1.java

// Patchwork
void setup()
{
  size(640, 640, P3D);
  noStroke();

  initialize();
}

void initialize()
{
  int count = (int) (1 / s);
  count *= count;
  current = new ArrayList( count );
  cx = width / 2; cy = height / 2;
  for(int i=0;i<count;i++)
  {
    current.add(i, 0);
  }
}

void triangle()
{
  pushMatrix();
   beginShape(TRIANGLES);
    fill(255);
    vertex(width, height, 0);
    vertex(0, height, 0);
    vertex(0, 0, 0);
    fill(0);
    vertex(width, 0, 0);
  endShape();
  popMatrix();
}

float cx, cy;
void triangleWithPosition(int p)
{
  pushMatrix();
  translate(cx, cy, 0);
  rotateZ(TWO_PI / 4. * p);
  //rotateZ(radians(frameCount));
  translate(-cx, -cy, 0);
  triangle();
  popMatrix();
}

void setPosition(int tile)
{
  current.set(tile, ((Integer)current.get(tile) + 1) % 4);
}

void mouseClicked()
{
  int numTiles = (int)(1 / s);
  int x = (int)Math.floor(((float)mouseX / width) * numTiles); 
  int y = (int)Math.floor(((float)mouseY / height) * numTiles);
  setPosition( y * numTiles + x );
}

void keyPressed()
{
  if(key == 'a')
  {
    s *= 0.5;
    initialize();
  } else if(key == 'z' && s < 1)
  {
    s /= 0.5;
    initialize();
  } else if(keyCode == KeyEvent.VK_SPACE)
  {
    int n = (int)random(0, current.size());
    setPosition(n);
  }
}

ArrayList current;
float s = 0.5;
void draw()
{
  int c = 0;
  background(0);
  scale(s, s);
  
  for(int j=0;j<height;j+=height*s) {
    for(int i=0;i<width;i+=width*s,c++) {
      pushMatrix();
        translate(i/s, j/s, 0);
        triangleWithPosition( (Integer)current.get(c) );
      popMatrix();
    }
  }
}

See http://play.taiste.fi/random/triangles.png for a sample image.