Supplementary Material

This page contains supplementary material for the paper entitled 'An Emergent Pattern Formation Approach to Dynamic Spatial Problems via Quantitative Front Propagation and Particle Chemotaxis'.


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:


PixieDust Framework Overview

Figure 1: A schematic illustration of emergent pattern formation processes in the PixieDust framework.



Figure 2: Multi-layered approach to spatial wavefront problems



Figure 3: Emergence of a stationary wave by projection and dissipation via quantitative diffusion. (3.2 MB)



Figure 4: Diffusive propagation from a simple point source (12.8 MB)



Figure 5, part 1: Front propagation is independent of orthogonal image layout (30.5 MB)



Figure 5, part 2: Front propagation from concave and convex stimuli occurs at same speed and continues to planar wave (13 MB)


Figure 6, part 1: Agent morphology in discrete version (left, 4 MB) and continuous angle version (right, 3.8 MB)




Figure 6, part 2: Very simple chemoattractive agent algorithm



Figure 7, part 1: Skeletonisation by front propagation and negative chemotaxis



Figure 7, part 2: Examples of skeletonisation of leaf, hand (1.4 MB) and body by front propagation and chemotaxis approach



Figure 8: Simulation of Adamatzky and Costello's chemical processor by emergent pattern formation (3 MB)



Figure 9, part 1: Front propagation from Voronoi point sources

Figure 9, part 2: Emergence of Voronoi diagram approximation by front propagation and negative particle chemotaxis (6.3 MB)



Figure 10, part 1: Voronoi stimulus induces internal skeleton result (3.9 MB)

Figure 10, part 2: Effects of increasing binary thresholds on Voronoi stimulus

Figure 10, part 3: Incorrect inversion of Voronoi diagram from binary Voronoi stimulus



Figure 11: Incorrect (top right) and more accurate (bottom left) inversion of Voronoi approximation by using entire greyscale range from emergent Voronoi diagram



Figure 12: Inversion of planar skeleton from simulated chemical processor to recover original planar shape location (2.3 MB)



Figure 13: Dynamic skeletonisation in response to a changing environment by emergent pattern formation (0.9 MB)



Figure 14, part 1: Dynamic Voronoi approximation by particle position when new point sources are added (11.6 MB)



Figure 14, part 2: Dynamic Voronoi approximation by particle position when point sources are removed



Figure 15: Dynamic Voronoi approximation from mobile point sources (7.4 MB)



Figure 16: Corrupted dynamic Voronoi approximation from mobile point sources that are moving too quickly (16.5 MB)



Figure 17: Simple path planning example (1.5 MB)



Figure 18, part 1: Front propagation through a maze (see below for video link)

Figure 18, part 2: Solutions to different mazes via front propagation and chemoattractive emergent pattern formation (50 MB)



Figure 19: Automatic dynamic response timeline to changing maze environment (17 MB)



Figure 20: Competition shifts the annihilation points of competing wavefronts
(The annihilation point movement and collapse can be seen in the previous video for fig 19 on the mark map window)



Figure 21: Annihilation point movement by channel constriction (4.4 MB)



Figure 22: Assigning costs to paths by channel constriction (7.5 MB)



Figure 23, part 1: Path choice in handmade version of Steinbock* maze is affected by constriction in non-uniform path channels (8.1 MB)

Figure 23, part 2: Path choice in uniform version of Steinbock* maze shows accurate shortest path (6.3 MB)


* Refers to original maze constructed and used in paper from Steinbock, Toth and Showalter: "Navigating complex labyrinths: optimal paths from chemical waves", Science, 267 (1995) 868-871.



Figure 24, part 1: Simple path through an open obstacle field (15.4 MB)

Figure 24, part 2: Two equally short paths emerge when path lengths are identical (14.2 MB)

Figure 24, part 3: Insufficient diffusion damping causes interference patterns, agent confusion and distorted paths (16.1 MB)



Figure 25: Path planning through complex obstacle field when agent start position changes

Figure 26: Changing the diffusion source location induces a backwards propagating shockwave in the swarm stream and momentary confusion before path is automatically reconfigured

Examples from Figures 25 and 26 (changing agent start position and diffusion start position) can be seen here. (165 MB)



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Material (c) Jeff Jones 2008