This is an illustration of the iterated function system used to obtain Heighway's fractal dragon (see e.g., Wikipedia page). At each stage, we apply to the current image U the transformations F1: rotate 45 degrees counter clockwise about the origin, and F2: rotate 135 degrees counter clockwise about (0.6,0.2). (Centres of rotations marked by little dots.) Take the union F1(U) + F2(U). Replace U by this and repeat ad infinitum. It doesn't really matter what image you start with; the attractor set is the same, so you'll get the same limit.