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.

Example

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.


Links at this site...
Links at other sites...
Created 13/10/99
Last modified 13/12/99