What was this new way of looking? At the same time that the iterative process had the
effect of overwhelming individual differences between functions, it also revealed a universality
in how large-scale features related to small details.

The shift in focus is from the particularities of a given function to the relation between different recursive levels in the iterative process.

Imagine two paintings, each showing an open door through which is revealed another open door,through which is revealed another and another....

One way to think about the doors in these two paintings is to focus on the particularities of the repeated forms. Suppose the doors of the first painting are ornately carved rectangles, whereas the second painting shows doors that are unadorned arches.

If we attend only to these shapes, the paintings might seem very different. But suppose we focus instead on the recursive repetition of doors in each painting and discover that in both paintings, the doors become smaller at a constant rate. Through this shift in focus, we have found a way of looking at the paintings that reveals their similarity to each other and to any other painting constructed in this way. The key is recursive symmetry.

From Chaos as Orderly Disorder: Shifting Ground in Contemporary Literature and Science by N. Katherine Hayles