Trees and Kanji

How many unrooted trees are there with N nodes? How many such that every node has one or three neighbors? One three or four? The latter two can be the basis for a Kanji style character system -- all characters are topologically different. How does it change if we permit loops? It begins to look a lot like the Sprouts game.

Another way of producing a system is to lay down some points, say a 4x4 grid, and consider the power set of all possible connections between them.

Consider a large grid of points. Edges drawn (or not drawn) to a point's eight neighbors allow the encoding of 4 bits (not 8 because edges are undirected). Choose 4 out of 8 neighbors such that no two are 180 degress across from each other. A larger local neighborhood allows a denser encoding -- thus bitwise enformation may be encoded in a spiderweb-like diagram.

A sentence may be grammatically parsed into a tree. If we establish a mapping between trees and (say) bits, information may be steganographically encoded in the grammar of a sentence as opposed to the semantics of the words it contains.