A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity (wikipedia).
James Gleick writes that 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 a bronchial branching proved to be quite wrong; a fractal description turned out to fit the data.
In the view of the Darwinists, the endlessly exquisite designs of nature are the result of an interplay of two factors - random genetic mutation and Natural Selection. Genetic mutation proposes, Natural Selection disposes. Some maintain that mutations usually detract from the viability of an organism and that Darwin's premise that genetic mutations are random is wrong. That is, that nature selects the strongest does not hold true.
The question of "design" in nature was one that troubled Charles Darwin. In the year following the publication of the Origin, he wrote, "I am conscious that I am in an utterly hopeless muddle. I cannot think that the world, as we see it, is the result of chance; and yet I cannot look at each separate thing as the result of design."
Design according to [Darwin] is Random Mutation + Natural Selection + Time. An awful lot of time. Regardless of the species, the changes over time have to come from changes in the Deoxyribonucleic acid (DNA). The entire plan for any organism is contained in its DNA, a molecule with 4 nucleobases. A strand of DNA can have anywhere from 500 thousand bases (in the case of the smallest known parasite) to about 3 billion for man and large animals.
So Darwinism says that random mutation or copying errors in the DNA produce a modified organism, and that natural selection weeds out less adaptable ones. What [remains] are new innovations in an organism design.
Of course, one of the difficulties with Darwinism is that it takes millions of years and many billions of organisms to produce significant change over time making it difficult to empirically prove Darwinism in the short lifetime of a human being.
In a totally different scientific discipline, mathematics, Benoit Mandelbrot‘s interest in irregular and seemingly chaotic patterns developed fractal geometry in the mid 1970’s. Sure a number of geometry systems have been developed since Euclidean geometry (c.300 B.C) fractals explore the infinitely complex shapes and self-similarity across scale featuring recursion – patterns seen everywhere in nature, economics, and cell biology (and here is the rub).
An example of this is a photograph of a section of coastline from a plane will show the same ragged contours as a photograph of the whole coast taken from a space station. A photograph of a one-foot-long section of the same coast will also show the same contours. The various coastlines are "self-similar," each similar to the others in shape, but different in magnitude.
Biologists began to find fractal organization controlling structures throughout the body. The standard exponential description of bronchial branching, for example, proved to be wrong; a fractal description turned out to fit the data. Other systems include the urinary collecting system, Biliary duct in the liver, network of special fibers in the heart that carry pulses of electric current to the contracting muscles.
