Since the forest is made of trees, and trees are a fractal shape, we can assume that the boundary of the forest is fractal. This has the consequence that the dog can't even get any distance into the forest before it is technically going out of it. To give a simple example, suppose the dog is outside the forest. It takes one step, then it happens to be under a leaf, so is therefore inside the forest. It takes another step, and it could be back under a piece of sky with a continuous path to the sky outside the forest, so is back out of the forest again!