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.
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.
This similarity may be useful in cases were the adjacency matrix is
- It may reduce the memory needed to analyse a chaotic system.
- It may allow some higher order pseudo-phase spaces (i.e. spaces
such as d(n),d(n+1) against d(n+1),d(n+2) or d(n),d(n+1),d(n+2)
against d(n+1),d(n+2),d(n+3)) to be generated with reduced memory
requirements. (Perhaps it will also allow other representation
methods for these higher order spaces.)
- It may allow mixed order pseudo-phase spaces to be generated.
(i.e. enable us to extract repeated streams of unequal length from
a number stream)
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Last modified 13/12/99