tails can be read in the shapes of our anatomical structures. One of the earliest observations of a mathematical relation in biology was that almost every living creature in every ecosystem on the planet, spanning more than 20 orders of magnitude in size from uni- to multi-cellular, has features that scale with the mass of the organism, including heart rate, life span, aorta size, tree trunk size, and metabolic rate. This is called allometric scaling.
A rule of thumb common in the halls of Intel was programmed into our bodies eons ago.
Strangely, the relationship between these features and an organism’s mass usually follows a power law. That means, for example, that metabolic rate depends on the organism’s mass, raised to some constant power. Even stranger, the constant for the majority of these features is some multiple of one fourth. Physicist Geoffrey West has argued that this scaling results from the ubiquity of fractal-like networks within organisms. Fractals are structures that have similar structure at very different spatial scales—one familiar example is the vasculature of a leaf, whose branching geometry is replicated in miniature across the leaf’s surface. They can be found in a dizzying variety of systems, including our nervous system, blood vessels, capillaries in plant leaves, lung bronchioles, the calyxes of kidneys, neurons, root systems, and mitochondrial cristae.
Why would nature use fractal geometry so regularly? Mathematically, fractals are interpreted as having a fractional dimension higher than the space they reside in: A fractal drawn on a two-dimensional sheet of paper, for example, has a higher dimension—say, 2.1. This is a useful feature, allowing nature to pack some part of a fourth dimension into three-dimensional space.
To see why it might be useful, we can turn to a well-known result in the semiconductor industry, called Pollack’s Rule. It states that the speedup achievable by adding computing elements to a processor is proportional to the number of added elements, raised to the power