Natural images are scale invariant. After a quick tutorial on percolation, I will talk about formulating a geometric view of scale invariance based on percolation theory. In this model, the scale invariance of natural images is understood as a second-order percolation phase transition. It is further quantified by fractal dimensions, and by anomalous exponents for the distribution of clusters in natural images. This formulation leads to a method for identifying clusters in images and a starting point for image segmentation.