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Wat, could it be that similar structures are due to being acted on by the same forces? Like gravity and/or the electromagnetic force? Both are long range forces that decrease proportionately with distance squared.
The closest I can think of are filaments of plasma in certain discharges, but even then it's rare to really get something very similar to the cosmic web or neurons. Besides that it's not common to see structures like this forming electromagnetically, because there are positive and negative electric charges, whereas mass always attracts. Electromagnetism is also much stronger, so the individual particles partnered up very quickly in the young universe, whereas the formation of structures due to gravity is an ongoing process, on scales both large and small.
Oh, I remember when you took beautiful images of these discharges! Hmm that does make it seem strange that they would be similar. Did you read the above study? It was just a pilot study, but the findings were interesting.
I was thinking also of how the structure of the atom (Bohr model) matches up with the solar system, but we know now of course the Bohr model isn't quite accurate but still the idea of (-) charge electrons orbiting around (+) charge protons does make one wonder about how forces that behave differently can sometimes result in similar structures.
This is pretty interesting stuff from the study:
The human brain functions thanks to its wide neuronal network that is deemed to contain approximately 69 billion neurons. On the other hand, the observable universe is composed of a cosmic web of at least 100 billion galaxies. Within both systems, only 30% of their masses are composed of galaxies and neurons. Within both systems, galaxies and neurons arrange themselves in long filaments or nodes between the filaments. Finally, within both systems, 70% of the distribution of mass or energy is composed of components playing an apparently passive role: water in the brain and dark energy in the observable Universe.
"We calculated the spectral density of both systems. This is a technique often employed in cosmology for studying the spatial distribution of galaxies," explains Franco Vazza. "Our analysis showed that the distribution of the fluctuation within the cerebellum neuronal network on a scale from 1 micrometer to 0.1 millimeters follows the same progression of the distribution of matter in the cosmic web but, of course, on a larger scale that goes from 5 million to 500 million light-years."
The two researchers also calculated some parameters characterizing both the neuronal network and the cosmic web: the average number of connections in each node and the tendency of clustering several connections in relevant central nodes within the network. "Once again, structural parameters have identified unexpected agreement levels. Probably, the connectivity within the two networks evolves following similar physical principles, despite the striking and obvious difference between the physical powers regulating galaxies and neurons," adds Alberto Feletti. "These two complex networks show more similarities than those shared between the cosmic web and a galaxy or a neuronal network and the inside of a neuronal body."