Nature is patterned, which is part of what makes a walk in the woods feel reassuring. The shapes of the branches are reflected in the veins of the leaves and the patterns of the paths between the trunks. The repeating patterns in fractals also seem to convey a logic or at least a pattern underlying the chaos. On the other hand, once you zoom in to a fractal, you have no way of knowing which level you are on. The details at one level of magnification may be the same as on any other.