Supplementary Material -

This page contains supplementary material for the paper entitled: 'Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks'


The material consists of electronic versions of the paper figures.

Links: Prefix 'VR Fxx' to video recordings of the experiments in action are available.

Note: Video recordings are in .mpg format using as generic as possible h264 encoding.


Paper Figures:


Figure 1: Plasmodium growth and protoplasmic vein formation in Physarum polycephalum
(Images courtesy of Andrew Adamatzky, UWE)



Figure 2: Layered approach of coupled maps used in the framework.




Figure 3: Base agent behavioural algorithm and agent morphology (top)
Coupling in gel mesh (bottom left) and streaming sol (bottom right)




Figure 4: Spontaneous formation and evolution of transport networks - RA 45, SA 22.5
VR F4a
VR F4b
VR F4c
VR F4d
VR F4e - temporary stable period late on in recording.




Figure 5: Stable minimising network approximates hexagonal tiling.
VR F5a - RA 45, SA 45 %p 15
VR F5b - RA 45, SA 45 %p 5





Figure 6: Increase of agent flux as cyclic structures close.
VR F6 (tracing a single particle movement during network formation)




Figure 7: Tracking of single agent particle shows characteristic shuttle streaming movement pattern.
VR F7 - Shuttle streaming movement in constrained corridor




Figure 8: Time taken to traverse entire lattice - population and agent
VR F8a - Complete coverage of lattice- whole population
VR F8b - Complete coverage of lattice - single agent




Figure 9: Formation of sheet-like structures from emergent networks and the emergence of dissipative vacancy islands
VR F9 - Plasmodial Sheet formation - vacancy islands
VR F9b - Vacancy islands at different scales
VR F9c - No plasmodial sheet due to branching behaviour



Figure 10: Effect of Sensor Offset distance (SO) on pattern scale and granularity.



Figure 11: Interaction between population size and sensory scale
Large version of tiled 300 x 300 lattices here (Warning! 2800 x 1650pixels and 3.4MB)




Figure 12: The effect of increasing population size and decreasing diffusion gradients on RA 45, SA 45 patterning
Large version of tiled 300x300 lattices here (Warning! 2178 x 2800 pixels and 800KB)




Figure 13: Patterns formed by chemo-attraction when varying SA and RA from zero to 180 degrees

Very Large version of tiled 500x500 lattices here (Warning! 4600 x 4600 pixels and 2.8MB)
Massive version from zero to 360 degrees in 22.5 degree increments on 500 x 500 lattices here (Warning! 8680 x 8680 pixels and 11 MB)




Figure 14: Examples of reticular, labyrinthine, island and hybrid/incomplete patterns from the parameter space mapping.
VR F14 - Long Term RA 45, SA 11.25
VR F14
- Long Term RA 45, SA 22.p
VR F14 - Long Term RA 22.5, SA 67.5
VR F14 - Long Term RA 45, SA 67.5
VR F14 - Long Term RA 90, SA 90




Figure 15: Patterns with chemo-repulsion behaviours formed by varying SA and RA from zero to 180 degrees

Very Large version of tiled 300x300 lattices here (Warning! 2800 x 2800 pixels and 8MB)




Figure 16: Evolution to regular periodic spacing in repulsive agents
VR F16a - Long Term Hexagons RA 45, SA 45
VR F16b - Long Term Stripes RA 67.5, SA 112.5
VR F16c - Long Term RA 157.5, SA 112.5




Figure 17: Visualisation of the effect of pre-patterning stimuli and the effect of stimuli weighting




Figure 18: Pattern formation and evolution under the influence of pre-patterning cues.
VR F18 - Pre-pattern 2 points



Figure 19: Approximation of Steiner minimum trees by evolving network in response to regular pre-pattern cues
VR F19a - Pre-pattern 3 points
VR F19b - Pre-pattern 4points
VR F19c - Pre-pattern 5points



Figure 20: Effects of reducing and increasing pre-pattern stimuli weights.
VR F20 - Effect of tightening / agent removal




Figure 21: Use of plasmodial sheet deformation method provides identical convergence and more regular results
VR F21b - Plasmodial Shrinkage - attempt 1
VR F21c
- Plasmodial Shrinkage - attempt 2
VR F21d
- Plasmodial Shrinkage - attempt 3
VR F21a - Filamentous condensation - 3 attempts (3 results shown on middle row)



Figure 22: Damage to uniform pattern is repaired to regenerate original pattern in chemo-repulsion based patterning
VR F22 - Damage Repair - Repulsive Behaviour




Figure 23: Damage to reticular network is repaired by chemo-attraction based patterning
VR F23 - Damage Repair - Attraction Behaviour




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Material (c) Jeff Jones 2008