 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 of (1-1/D), where D is the dimension in which the processors are arranged. A three-dimensional arrangement of, say, 100 processors will give a greater boost than a two-dimensional arrangement of those same processors, due to reduced signal latency. The same kind of speedup can be achieved in our nervous and circulatory systems with a D of greater than three. A rule of thumb common in the halls of Intel was programmed into our bodies eons ago; the fractal arrangement of our biological sensors and the nerves that connect them are designed for speed.
The brain represents the height of biological information processing and transmission. But for years, it’s been considered a noisy instrument. Neurons code information with binary electrical events called spikes, shocking one another like tiny batteries. Once a neuron receives enough input that its voltage passes a certain threshold, it will spike in turn, sending its signal to downstream neurons. Fluctuations in the summed output of the brain’s 100 billion neurons, as measured by an electroencephalogram, or EEG, are much smaller than the amplitude of individual spikes, and were long thought to be epiphenomenal: pointers to various brain states, but not an information-carrying signal in itself. In other words, noise.
Slow oscillations in the brain are coherent over large anatomical distances, in the same way you can hear the bass from your neighbor’s sound system better than the treble.
Yet, as we saw with genetic expression, interactions among many discrete elements can be incredibly useful. It’s becoming clear that the so-called noise seen in an EEG is actually an important signal, and one that is crucial to neural computation. The fluctuation of the summed output of the brain’s neurons feeds back to affect the resting potential of those neurons, bringing them closer to or farther from spike threshold. Slow oscillations (as found in drowsy or sleeping animals) are coherent over large anatomical distances, in the same way you can hear the bass from your neighbor’s sound system better than the treble. This is how the brain may be facilitating communication between disparate brain areas: If an individual spike is timed with the crest of the slow amplitude fluctuation, it will have a bigger effect downstream than if it is timed with a trough. Neurons are somehow coordinating themselves to generate self-directed, global feedback that serves to adaptively boost even sub-detectable signals: No informational signal is wasted.
In fact, it is an open question whether the idea of “waste” can even be properly defined in the context of the brain. Theoretical neuroscientist Tony Bell argues that the hallmark of biological computation is that information flows across multiple hierarchies of complexity, bubbling up from microscopic to macroscopic levels and back down again.
Simpler structures (like neurons) communicate with more complex structures (like areas of the brain), and vice versa. Computations are occurring on and between every level, from molecules to cells to organisms as a w