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## WHAT IS IT?

fuzzylumps05.nlogo, 06 august 2006

by ralph abraham, UC santa cruz, abraham@vismath.org

with sisir roy, ISI calcutta, sisir@isical.ac.in

In this model, we simulate the dynamical cellular network (DCN) of nodes

and bonds, as described in Requardt and Roy, 2001. Fuzzy lumps (emergent supernodes and superbonds) and the clique graphs will come later.

## HOW IT WORKS

An initial random distribution of node and bond states evolves according to a dynamical rule. See the model description document (PDF) on our website.

NOTE: The origin (0, 0) for indices (i, k) is at the lower right corner of the graphics window. In this preliminary version there are 18 nodes, numbered from 0 to 17.

There are four display modes:

"bonds" displays bond-states, J_ik, as colored squares above the diagonal

"nodes" displays node-differences, s_ik as colored squares above the diagonal

"digraph" displays a green square (for "1") above and below the diag

"graph" displays a cyan square (for "1") above and below the diag

In each case, the node-states, s_i, are displayed on the diagonal as colored circles.

## HOW TO USE IT

Just press "setup" and "step" or "go" as usual.

To display attributes:

1. Press go to stop the simulation;

2. Change the display option with the "display-matrix" drop-down menu; and

3. Press the button "update-display" to change the display type.

Again press "step" or "go".

To display the permutation of the current graph:

1. Press "go" to stop the simulation;

2. Press "show-weight-list".

Then three consecutive lines are shown in the "Command Center":

A. the list of pairs, (node-number, node-weight), in order of node-number,

B. the list A sorted by decreasing weights, and

C. the list of node numbers of list B, that is, the permutation of the graph

## THINGS TO NOTICE

See if any stable attractors emerge.

## THINGS TO TRY

Move sliders and begin a fresh run.

## EXTENDING THE MODEL

Fuzzy lumps are coming later. Our plan is to run the model until an attractor is reached, then export a permutation to an external program such as Combinatorica to find its cliques and weights, and then submit this data to another NetLogo model to self-organize the cliques and weights as supernodes aproximating an isometric embedding.

## NETLOGO FEATURES

Agents are useful for the emergence of supernodes

## RELATED MODELS

See Nowotny, dissertation.

## CREDITS AND REFERENCES

Requardt and Roy, 2001