If you clip off a cluster of branches from the end of a limb and hold it up by its own “trunk,” it resembles a miniature tree in its own right. Thus, trees are often self-similar—the parts resemble the whole.
Not that such match-ups would necessarily be exact. Nature yields only approximate fractals. True fractals, with perfect self-similarity, are found only in mathematics. Famous examples are the intricate Koch curve (formed by repeatedly removing the middle thirds of triangles’ sides and replacing them with smaller triangles) and the exuberant Mandelbrot set (a lacy design etched out through a special algorithm). Still, the existence of almost scale-free natural structures could reveal critical clues about the hidden architecture of reality’s cathedral.
A number of researchers have suggested that the universe itself is a fractal. One of the pioneers of such a hierarchical approach is Robert Oldershaw of Amherst College, who has published numerous papers on the subject. Through comparing the properties of systems on many scales, he “found that there was a considerable potential for physically meaningful analogies among atomic, stellar, and galactic scale systems.”
Oldershaw has speculated that nature’s hierarchy continues indefinitely—like an unlimited succession of Russian dolls, nested one inside the other. Why assume that galactic superclusters are the highest form of organization in the kingdom of all possibilities? Perhaps, he has suggested, the observable universe comprises but a metagalaxy in a greater realm—a meta-metagalaxy, so to speak. The meta-metagalaxy, in turn, would constitute part of an even larger entity, and so on.
In this spirit, let’s construct our own cosmic hierarchy. We divide astronomical objects into seven major classes, covering an enormous range of sizes. The first class includes asteroids, comets, and other types of “minor planetary objects,” ranging from several feet to hundreds of miles across. Second come planets, with radii spanning