Supplementary Material - Emergence of Transport Networks

This page contains supplementary material for the paper entitled: 'The Emergence and Dynamical Evolution of Complex Transport Networks from Simple Low-Level Behaviours'


The material consists of electronic versions of the paper figures.

Links (where underlined) to video recordings of the experiments in action are available.

Note: To view the lossless compressed video, the Techsmith CODEC may be required. This can be downloaded by clicking here.


Paper Figures:


Figure 1: Top-down vs. Bottom-up approaches to modelling of complex systems.





Figure 3: Emergence of a persistent dynamical network




Figure 4: Emergence of a dynamic equilibrium state with sensor angle of 45 degrees.



In text reference: Re-emergence of foraging state from stable state



Figure 5: Surface minimisation on fixed boundaries with adhesion in the corner areas.




Figure 6: Surface minimisation without adhesion




Figure 7: Initial aggregation caused by diffusion and chemotactic movement




Figure 8: Differences in agent flow at the inside and outside of a network path cause circular loop contraction.





Figure 9: Evolution of branching and streaming behaviour when SA is 15 degrees.
(see the above re-emergence video) for streaming and anastomosis




Figure 10: Network length problem datasets
Dots represent parts of landscape where diffusive trail is introduced at the network nodes.




Figure 11: Network minimisation by filamentous shrinkage on 2, 3, 6 and 7 node networks.

1 - Two points
2 - Triangle (experiment repeated 3 times)
3 - Domino 6 points
4 - Seven points




Figure 12: Incorrect minimisation of network using filamentous shrinkage.




Figure 13: Network collapse when network node sources are removed




Figure 14: Network minimisation using filamentous foraging approach

1 - Three Points
2 - Six Points
3 - Seven Points




Figure 15: Evolution of the plasmodial shrinkage method.
(Dark spots indicate node diffusion points. Small flecks indicate dynamic fluctuations in the density of the trail 'sheet'.)

1 - Three Points
2 - Nested Hexagons
3 - Four x Four Grid
4 - Seven Points




Figure 16: Approximation of concave hull and TSP tour using plasmodial shrinkage.

1 - Cross Pattern of 12 Nodes
2 - Ten Nodes Perimeter




Figure 17: Cyclic and erroneous minimisation and dynamic remodelling

Top Row:
Erroneous network minimisation using filamentous condensation with cycles formed (columns 1-3). Erroneous minimisation of 64 regular nodes using plasmodial shrinkage caused by instabilities in the deforming sheet (Column 4)
Bottom Row:
Continuous network remodelling by foraging behaviour in filamentous condensation.


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Material (c) Jeff Jones 2008