The cosmic web is what we call the network of filaments between neighboring galaxies, and the membranes between these filaments. It has various descriptions; a dual description is a network of bubbles called voids, which expand at different rates and collide. Filaments, membranes, and galaxies arise at the interfaces of these bubbles; the matter flows analogously to how water flows on a landscape (I will mention some of our recent work about the cosmic equivalent of a “rainstorm”). Channels of matter (water, in the case of a river, or gas and dark matter, in the case of a filament) form where matter collects with other matter that may have originated far away. Channels form between literal hills on earth, or hills of the gravitational potential, in the cosmos. I will discuss some work about the identical geometric description of the cosmic web and structural spiderwebs, which are networks that can be strung up entirely in tension. Through a formalism called graphical statics, of which James Clerk Maxwell was a founding figure, structural spiderwebs naturally arise when material collects at interfaces between bubbles. I will also discuss some software employing this formalism, and the relationship between these structures and biological branching structures such as trees.