Dendritic arborization is the term for how the neuron develops its characteristic tree-like structure. Similar tree-like structures are found throughout the human body: the bronchii of the lungs, blood vessels,  in the arrangement of delicate strings of messenger RNA as they are transcribed from DNA, the branching glycogen molecules that serve as a form of energy storage in the liver and skeletal muscle, and in the arbor vitae—the beautifully branching white matter tracts—of the cerebellum.

It is thought that arborescent cell structures form by repeated cell division in one straight line until a genetically programmed split, or bifurcation, happens. In the case of the neuron, which itself is a single cell, arborization and bifurcation of its projections are thought to arise from repeated electrochemical signaling events. Form flows from function. Repeated bifurcations, both self-directed and in response to physical obstacles in the environment, yield these breathtaking branching structures that are seen throughout the living world.

Arborescence is not limited to biology, though. It is a phenomenon that has been observed even in the large-scale structure of the cosmos. Scientists began discovering what are called galaxy filaments in the late 1980s—the largest known structures in the universe. These web-like formations are typically 200 million light years across (our Milky Way galaxy, by comparison, is but 100,000 light years across) and consist of galaxies bound together by gravity between massive voids of empty space. 

The natural sciences are not alone in their enchantment with dendritic modes. Indeed, artists have also noticed nature’s stochastic forms, particularly in the 20th century. Kazimir Malevich’s 1915 painting Black Square, even in its pure abstraction, reproduces the webbed pattern. Early 20th century Dutch painter Piet Mondrain's less well-known work centered around contorted branches, and it is said that he actually found them disturbing. German abstractionist Wols explored entirely non-representational branching forms in his early work. And arborescence repeatedly emerges in the work of the more famous Jackson Pollock.

Does the arborescent form simply emerge at different scales from superstructures made of more fundamental components of the universe? Might the fundamental components of the universe themselves be made of, or result from, some kind of repeating eigenshape?