Consider the fern. A fern is composed of individual fronds. Each frond is composed of smaller, more intricate designs. What is fascinating is that on whatever scale you view it—a part of a frond, an entire frond, or a fern as a whole—the design is identical. Thus, a small part of the figure when enlarged reproduces the original figure; the figure of the fern is created by repeating the same pattern at smaller and smaller scales. In other words, the part contains the whole.
The relative complexity of the fern is thus the same regardless of scale. An object with this quality is referred to as being “scale insensitive.” The French-American mathematician Benoit Mandelbrot first described this concept. Mandelbrot had expanded on the work of Lewis Richardson, a mathematician who had discovered problems in trying to measure the coastline of England. If you view the coastline from an orbiting satellite, it would generally appear jagged, but you would see some stretches that appear smooth. With a view from an altitude of 5,000 meters, however, you would find that the smooth parts are actually mostly jagged, with some smooth parts. You would obtain the same results at successive levels of magnification—that is, a photo taken from ten centimeters above the coastline will reveal the same relative degree of jaggedness and smoothness as a picture taken from outer space. Mandelbrot described this phenomenon as a “fractal”: “[A] geometric shape that can be separated into parts, each of which is a reduced-scale version of the whole.”
Read more from the most recent On Remand article, America the Eusocial by Timothy P. O’Neill here.