**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:**

**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

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Material (c) Jeff Jones 2008