Abstract: First I will describe a class of networks with geometries based on a particular generalization of a Voronoi diagram. In https://arxiv.org/abs/1710.04509, we discussed a few networks in this class: the cosmic web (the large-scale spatial arrangement of matter in the universe); spiderwebs, structural-engineering networks that can be strung up to be either entirely in tension (like a spiderweb) or entirely in compression (like a tree); and origami tessellations. Other networks likely fall into this class, and I would love to hear what some SFI members think.
Also, I will briefly describe what happens to 'primordial information' as the cosmic web forms. The standard picture is that in the first instants of the universe, just after the Big Bang, a pattern of random quantum density fluctuations was laid down, called primordial information. In patches that form the cosmic web, the small-scale primordial information inside them is at least partially lost. The pattern of fluctuations provides a blueprint for the deterministic and one-to-one formation of structures on large scales. At small scales, the structure is no longer deterministic, and it is an open question where this boundary in scale lies.