DNA can be seen as a permanent information storage system for regulating the myriads of chemical reactions in the body. It guides the system as a whole and replicates itself when necessary. Thus, DNA is at once a product of a long history of chemical evolution and a driver of future evolutionary change.
Benoit Mandelbrot, the mathematician, noticed that similar chaotic but orderly systems existed in widely different scientific discipline. He had originally been working on the distribution of large and small incomes in an economy and had made a diagram of the peculiar relationships he had noticed in the figures. When he was invited to give a talk on his findings at Harvard, he saw an identical diagram on an economist's blackboard. But the diagram represented cotton prices.
He became curious. So, he studied cotton prices which dated back over a century on the New York futures exchange and discovered that the same pattern of change recurred over and over in different time frames. Patterns of daily, monthly, and yearly price changes matched perfectly, even though each particular price was unpredictable.
Mandelbrot continued to look for, and find, that pattern everywhere. He studied coastlines and discovered that at each level of magnification the coastlines retained the same complex assortment of bays and peninsulas. As in the cotton price data, coastlines contain the same amount of detail at all scales.
Mandelbrot was on his way to defining fractal geometry.
Gleick explains that the word "fractal" is derived from the Latin "fractus," meaning "broken." It is also related to the English words "fracture" and "fraction," which accurately reflect how fractal geometry breaks up the world and reconnects it with its own rules. Euclidean geometry describes lines, planes, squares, and spheres--abstractions of universal shapes. But reality is filled with rough, jagged surfaces. Fractal geometry deals with these.
Fractals consist of nested patterns. The overall structure is repeated with some variation all the way to infinity. There is no loss of detail even at high magnification. Consider the most striking form of fractals--the Mandelbrot Set. This set is a collection of points on a graph generated by taking a complex number, squaring it, adding the first number, squaring it--over and over again. If the number remains finite, it's in the set.
Gleick conveyed his astonishment at the beauty of these fractals: "The Mandelbrot Set is the most complex object in mathematics, it's admirers like to say. An eternity would not be enough time to see it all, its disks studded with prickly thorns, its spirals and filaments curling outward and around, bearing bulbous molecules that hang, infinitely variegated, like grapes on God's personal vine."
Just as the Mandelbrot Set contains large numbers of shapes in a small area, it is possible to pack a vast amount of area into a small volume by using three-dimensional fractals. This is exactly what biological systems do. Miles of veins and arteries, and arrays of nerve cells are arranged artfully in a human body. Acres of bronchial tissue are layered into a pair of lungs. Muscle cells in the heart and neurons in the brain also show fractal organization.
Tree branches, leaves, roots, snowflakes, cloud formations, mountain ranges, river systems, and galaxies all show the distinct pattern within pattern which is the mark of fractal geometry. Fractal geometry can be found everywhere in nature. Apparently it is one of the most efficient ways to arrange matter.
Fractals can also be used to model events happening in time, such as changes in cotton prices and the weather. This amazing versatility can be explained if fractals are thought of as abstract pictures of the self-organizing forces of nature. In this respect, fractal geometry strongly resembles information theory. The unpredictability of its parts allows it to generate information while its overall redundant structure protects the message it bears.
The double helix of DNA can be seen as a fractal that acts as an information storage and retrieval system. It codes for redundancy. It constructs a body, each cell of which contains enough information to construct another body. DNA tells messenger RNA to "create this structure--over and over again," allowing life to preserve and transmit its message to the future.
Cooperative behavior can emerge from the apparently random activities of very simple creatures. Such creatures don't possess nearly enough of the required brainpower to be able to make conscious choices, while cooperative behavior from our human vantage point normally indicates the presence of choice.
Prigogine and Stengers describe how the construction of a termites' nest actually appears to start as disorderly activity: "At this stage, they transport and drop lumps of earth in a random fashion, but in doing so they impregnate the lumps with a hormone that attracts other termites.... As termites become more numerous in a region, the probability of their dropping lumps of earth there increases, leading in turn to a still higher concentration of the hormone. In this way 'pillars' are formed, separated by a distance related to the range over which the hormone spreads."
The termites continue to build up their nest in this way while being guided by the ever-increasing amounts of hornome in the work areas. A disorderly activity becomes orderly dues to exponentially rising activity in specific sites chosen randomly. Thus, a complex structure, such as a termites' nest, can grow from the efforst of individuals with little information on what other individuals are doing and with no central planning.