Chaos: Making a New Science

by James Gleick

Blood vessels, from aorta to capillaries, form another kind of continuum. They branch and divide and branch again until they become so narrow that blood cells are forced to slide through single file. The nature of their branching is fractal. Their structure resembles one of the monstrous imaginary objects conceived by Mandelbrot’s turn-of–the-century mathematicians. As a matter of physiological necessity, blood vessels must perform a bit of dimensional magic. Just as the Koch curve, for example, squeezes a line of infinite length into a small area, the circulatory system must squeeze a huge surface area into a limited volume. In terms of the body’s resources, blood is expensive and space is at a premium. The fractal structure nature has devised works so efficiently that, in most tissue, no cell is ever more than three or four cells away from a blood vessel. Yet the vessels and blood take up little space, no more than about five percent of the body. It is, as Mandelbrot put it, the Merchant of Venice Syndrome—not only can’t you take a pound of flesh without spilling blood, you can’t take a milligram. This exquisite structure—actually, two intertwining trees of veins and arteries—is far from exceptional. The body is filled with such complexity. In the digestive tract, tissue reveals undulations within undulations. The lungs, too, need to pack the greatest possible surface into the smallest space. An animal’s ability to absorb oxygen is roughly proportional to the surface are...