Discrete Dynamics Lab
Examples of the network graph and the attractor jumpgraph
A new feature in DDLab is a graph with weighed vertices and
weighted directed
edges, which can be rearranged by dragging vertices. There are also
various other methods for investigating and manipulating the graph,
which can also be presented as a link table or matrix.
The graph is applied in two ways.
 To represent the RBN or CA network itself.
 As an attractor jumpgraph, which shows the probability of
jumping between basins of attraction caused by 1bit flips to
attractor states, giving an idea of the stability and mobility between
basins of attraction subject to noise.
The algorithm in DDLab version 23 contained an error in
computing the jumpgraph, so please update to version 24 where the error
is fixed.
Both types of graph show nodes linked by directed edges,
where the outgoing edge is colored the same as its
parent node. Both the nodes and edges are scaled,
for networks graphs according to k, for attractor jumpgraphs
according to basin volume,
the fraction of statespace in each basin.
The full width of the outgoing links is then apportioned according
to the jump probabilities.
The stubs on nodes indicate self links.
Click on each image to see it full size.


The graph as it first appears.
 The same graph rearranged by dragging vertices with the mouse.

Fig 1. A graph of an RBN network, n=33 with a
powerlaw distribution
of both k and outdegree,
which is biased according to k. The power law exponent is 2.
Nodes and edges are scaled according to k.



The network graph as it first appears.
 The same network graph rearranged by dragging vertices with the mouse.

Fig 2. A graph of an RBN network, n=10, k=3.
Nodes and edges are scaled according to k.
Its attractor jumpgraph is shown below.



The attractor jumpgraph as it first appears.
 The same attractor jumpgraph rearranged by dragging
vertices with the mouse.

Fig 3. The attractor jumpgraph of the network in fig.2.
There are 9 basins. Nodes and edges are scaled according to basin volume,
the fraction of statespace in each basin.


Fig 4. The attractor jumpgraph with the relevant basins of attraction drawn
inside each node.


Fig 5. Above, the network graph of a 1d CA, n=10, rule 141.
The attractor jumpgraph of the network is shown below.



The attractor jumpgraph as it first appears.
 The same attractor jumpgraph rearanged by dragging
vertices with the mouse.

Fig 6. The attractor jumpgraph of the network in fig.5.
There are 18 basins. Nodes and edges are scaled according to
basin volume, the fraction of statespace in each basin.


Fig 7. The jumpgraph with the relevant basins of attraction drawn
inside each node.

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Last modified: May 2002