Chaos - James Gleick [52]
Not immediately, but a decade after Mandelbrot published his physiological speculations, some theoretical biologists began to find fractal organization controlling structures all through the body. The standard “exponential” description of bronchial branching proved to be quite wrong; a fractal description turned out to fit the data. The urinary collecting system proved fractal. The biliary duct in the liver. The network of special fibers in the heart that carry pulses of electric current to the contracting muscles. The last structure, known to heart specialists as the His-Purkinje network, inspired a particularly important line of research. Considerable work on healthy and abnormal hearts turned out to hinge on the details of how the muscle cells of the left and right pumping chambers all manage to coordinate their timing. Several chaos-minded cardiologists found that the frequency spectrum of heartbeat timing, like earthquakes and economic phenomena, followed fractal laws, and they argued that one key to understanding heartbeat timing was the fractal organization of the His-Purkinje network, a labyrinth of branching pathways organized to be self-similar on smaller and smaller scales.
How did nature manage to evolve such complicated architecture? Mandelbrot’s point is that the complications exist only in the context of traditional Euclidean geometry. As fractals, branching structures can be described with transparent simplicity, with just a few bits of information. Perhaps the simple transformations that gave rise to the shapes devised by Koch, Peano, and Sierpiński have their analogue in the coded instructions of an organism’s genes. DNA surely cannot specify the vast number of bronchi, bronchioles, and alveoli or the particular spatial structure of the resulting tree, but it can specify a repeating process of bifurcation and development. Such processes suit nature’s purposes. When E. I. DuPont de Nemours & Company and the United States Army finally began to produce a synthetic match for goose down, it was by finally realizing that the phenomenal air-trapping ability of the natural product came from the fractal nodes and branches of down’s key protein, keratin. Mandelbrot glided matter-of-factly from pulmonary and vascular trees to real botanical trees, trees that need to capture sun and resist wind, with fractal branches and fractal leaves. And theoretical biologists began to speculate that fractal scaling was not just common but universal in morphogenesis. They argued that understanding how such patterns were encoded and processed had become a major challenge to biology.
“I STARTED LOOKING in the trash cans of science for such phenomena, because I suspected that what I was observing was not an exception but perhaps very widespread. I attended lectures and looked in unfashionable periodicals, most of them of little or no yield, but once in a while finding some interesting things. In a way it was a naturalist’s approach, not a theoretician’s approach. But my gamble paid off.”
Having consolidated a life’s collection of ideas about nature and mathematical history into one book, Mandelbrot found an unaccustomed measure of academic success. He became a fixture of the scientific lecture circuit, with his indispensable trays of color slides and his wispy white hair. He began to win