Human ecology
Graph theory
Pseudo-phase spaces
Graphs of pseudo-phase-spaces

A pseudo-phase space of a discrete number stream is in similar to the adjacency matrix of a graph. This similarity is based on two factors. First, taking the digits of the number stream as the vertices of the graph. Secondly, taking the digit changes (d(n),d(n+1)) as edges connecting the vertices. The main difference is that the pseudo-phase space makes the number of connections between each vertice pair explicit, whereas an adjacency matrix usually records only the presence or absence of an edge.


A picture that looks a bit like a 
ball of string

This is a graph of the same equation that I used for the pseudo-phase space example (the logistic map for lambda = 3.995). The main difference is that this example groups the x values into 50 intervals rather than the 16 used before. The vertices are the 50 points grouped in a circle. The edges are the lines connecting the points.

Conjectures This similarity may be useful in cases were the adjacency matrix is sparse.

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Created 13/10/99
Last modified 13/12/99