Many of nature’s fractal objects benefit from the favorable functionality that comes from pattern repetition at various sizes. Examples from nature include beaches, lightning, rivers, and trees, as well as cardiovascular and respiratory systems such as the bronchial tree. Neurons, like trees, are thought to represent a common kind of fractal branching activity.
Although prior neuron research has calculated the scaling characteristics of their dendritic branches, this has generally been done to categorize neuron morphologies rather than quantify how neurons benefit from their fractal geometry.
Why does the body use fractal neurons rather than, say, the Euclidean wires seen in common electronics? Within the mammalian brain, neurons create vast networks, with individual neurons utilizing up to 60,000 connections in the hippocampus alone. They link to the retina’s photoreceptors, letting humans see, and to the limbs, allowing people to move and feel, in addition to their connections within the brain. Given its relevance as the body’s “wire,” the study focuses on the effect of fractal scaling in creating neuron connections.
“By distorting their branches and looking at what happens, we were able to show that the fractal weaving of the natural branches is balancing the ability of neurons to connect with their neighbors to form natural electric circuits while balancing the construction and operating costs of the circuits,” Rowland said.
Nature’s fractals benefit from the fact that they develop at various sizes, according to Taylor, who has long looked to fractals for bioinspiration. While trees are the most well-known example of fractal branching, he claims that this research shows how neurons vary from trees.
“Whereas the fractal character of trees originates predominantly from the distribution of branch sizes, the neurons also use the way their branches weave through space to generate their fractal character.”
Taylor, a Cottrell Scholar of the Research Council for Science Advancement, was given a broad U.S. patent in 2015 for not just his vision-related artificial fractal-based implants, but also for any such implants that link signaling activity with nerves for any purpose in animal and human biology.
How neurons exploit fractal geometry to optimize their network connectivity, Julian H. Smith, Conor Rowland, B. Harland, S. Moslehi, R. D. Montgomery, K. Schobert, W. J. Watterson, J. Dalrymple-Alford & R. P. Taylor
Published: January 2021, Scientific Reports volume 11, Article number: 2332