Processing - why does my Random Walker always tend toward the top left?

I am currently going through Daniel Shiffman's 'The Nature Of Code', and have been playing around with one of the first exercises - a simple 'RandomWalker()'. I have implemented similar things in Java & had no trouble, however for some reason my walker always seems to go in more or less the same direction:

RandomWalker

This happens 100% of the time. Here is my code:

class Walker
{
  int x;
  int y;

  // Constructor

  Walker()
  {
    x = width / 2;
    y = height / 2;
  }

  void display()
  {
    stroke(0); // Colour
    point(x, y); // Colours one pixel in
  }

  void step()
  {
    float stepX;
    float stepY;

    stepX = random(-1, 1);
    stepY = random(-1, 1);

    x += stepX;
    y += stepY;
  }
}

Walker w;

void setup()
{
  size(640, 360);
  w = new Walker();
  background(255);
}

void draw()
{
  w.step();
  w.display();
}

Is this some artefact of the random function? My first thought is that it's something to do with the pseudorandom nature of the function but the textbook specifically states that this should not be noticeable, and yet this happens every single time. I was wondering if maybe there's something wrong with my code?

Thanks in advance.