Chaos - James Gleick [107]
“EVERYTHING WAS VERY GEOMETRIC straight-line approaches,” said Heinz-Otto Peitgen. He was talking about modern art. “The work of Josef Albers, for example, trying to discover the relation of colors, this was essentially just squares of different colors put onto each other. These things were very popular. If you look at it now it seems to have passed. People don’t like it any more. In Germany they built huge apartment blocks in the Bauhaus style and people move out, they don’t like to live there. There are very deep reasons, it seems to me, in society right now to dislike some aspects of our conception of nature.” Peitgen had been helping a visitor select blowups of regions of the Mandelbrot set, Julia sets, and other complex iterative processes, all exquisitely colored. In his small California office he offered slides, large transparencies, even a Mandelbrot set calendar. “The deep enthusiasm we have has to do with this different perspective of looking at nature. What is the true aspect of the natural object? The tree, let’s say—what is important? Is it the straight line, or is it the fractal object?” At Cornell, meanwhile, John Hubbard was struggling with the demands of commerce. Hundreds of letters were flowing into the mathematics department to request Mandelbrot set pictures, and he realized he had to create samples and price lists. Dozens of images were already calculated and stored in his computers, ready for instant display, with the help of the graduate students who remembered the technical detail. But the most spectacular pictures, with the finest resolution and the most vivid coloration, were coming from two Germans, Peitgen and Peter H. Richter, and their team of scientists at the University of Bremen, with the enthusiastic sponsorship of a local bank.
Peitgen and Richter, one a mathematician and the other a physicist, turned their careers over to the Mandelbrot set. It held a universe of ideas for them: a modern philosophy of art, a justification of the new role of experimentation in mathematics, a way of bringing complex systems before a large public. They published glossy catalogs and books, and they traveled around the world with a gallery exhibit of their computer images. Richter had come to complex systems from physics by way of chemistry and then biochemistry, studying oscillations in biological pathways. In a series of papers on such phenomena as the immune system and the conversion of sugar into energy by yeast, he found that oscillations often governed the dynamics of processes that were customarily viewed as static, for the good reason that living systems cannot easily be opened up for examination in real time. Richter kept clamped to his windowsill a well-oiled double pendulum, his “pet dynamical system,” custom-made for him by his university machine shop. From time to time he would set it spinning in chaotic nonrhythms that he could emulate on a computer as well. The dependence on initial conditions was so sensitive that the gravitational pull of a single raindrop a mile away mixed up the motion within fifty or sixty revolutions, about two minutes. His multicolor graphic pictures of the phase space of this double pendulum showed the mingled regions of periodicity and chaos, and he used the same graphic techniques to display, for example, idealized regions of magnetization in a metal and also to explore the Mandelbrot set.
For his colleague Peitgen the study of complexity provided a chance to create new traditions in science instead of just solving problems. “In a brand new area like this one, you can start thinking today and if you are a good scientist you might be able to come up with interesting solutions in a few days or a week or a month,” Peitgen said. The subject is unstructured.
“In a structured subject, it is known what is known, what is unknown, what people have already tried and doesn’t lead