CS420 Project 2
Creation of Spatial Structure by Activator/Inhibitor
Cellular Automaton
Alexander Saites
2/17/2012
Alexander Saites
1
Introduction
In this experiment, I wrote a Matlab program to simulate a group of Activator/Inhibitor cellular
automaton, using the values J1, J2, R1, R2, and h to each represent activation, inhibition, activation
radius, inhibition radius, and bias, respectively. By setting J1=1 and J2=-0.1, I systematically varied R1,
R2, and h while noting their spatial structures. The program simultaneously simulated five different
groups of cells, each with a different random starting state. Additionally, I had my program calculate the
average correlation, average joint entropy, and average mutual information for each set of five groups
of cells. This information was plotted alongside the experiments and was considered during analysis.
Experiments
I performed experiments using the following parameter values. Each experiment involved five random
groups of cells, each with a different, random starting position. During each I cycle, my program
randomly chose a cell to be updated. This continued until all cells had been updated. During each
update cycle, the number of updated cells is recorded. The procedure continues until cells are no longer
updated (i.e., convergence).
R1
1
1
1
1
1
1
1
2
2
2
3
3
3
7
8
12
1
1
1
1
1
1
1
1
1
2
2
R2
4
2
5
5
5
9
14
5
5
9
9
9
14
9
14
14
2
3
5
6
7
2
2
2
2
3
4
h
1
0
-4
-2
0
0
0
-1
0
-6
-3
0
0
0
0
0
0
0
0
0
0
-1
-2
1
2
0
0
Alexander Saites
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
6
6
6
6
6
6
7
7
7
7
7
7
7
7
10
10
10
10
10
13
13
2
5
6
7
8
9
10
4
6
8
10
12
15
4
5
8
11
11
8
13
8
10
13
9
11
14
8
01
13
8
10
12
14
14
14
12
14
14
0
0
0
0
0
0
0
0
0
0
0
-1
-1
-2
-2
0
0
0
-1
-1
-1
0
0
9
-1
-1
-1
-3
-3
0
0
-1
-4
-4
0
-5
Analysis
Throughout these experiments, I made judgments about how the parameters affected the spatial
structure. The proceeding paragraphs summarize these findings and offer selected images to support
them.
Alexander Saites
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As R1 and R2 get farther apart, sections that are more distinct seem to appear. When they are close
together, but at a median value, the pattern tends to converge to either only black or only white. We
should expect many distinct sections to appear when R1=1 and R2=14, and in fact, no pattern seems to
emerge and the cells do not converge.
As R2 is varied, Average joint entropy and average mutual information stay about the same. However,
Average Correlation begins to develop a "hump", implying that there are either spots or stripes
developing. This is consistent with the idea above, that sections that are more distinct appear as R1 and
R2 get farther apart. Indeed, when R1 and R2 are farther apart, "humps" appear in the average
correlation, and spots or stripe-like patterns appear.
Alexander Saites
4
For values R1 and R2 that are far enough apart for spots or stripes, bias plays a major role in the
development of spots. Specifically, biases with higher absolute values result in large sections of one
color with progressively smaller spots of the other. This is expected, as the bias obviously causes cells to
be more likely to turn one way or the other, while the differences in radii result in the development of
distinct sections.
Alexander Saites
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To get a few, small spots, use a large bias (in terms of absolute value, around 4), keep the difference
between R1 and R2 moderate (about 5), and keep the values in a mid-range (between around 4 and 10).
If the radii are in a smaller range, you will get many very small spots, unless the radii are too close
Alexander Saites
together, in which case you will likely converge to a solid color. If the radii are too large, you will get
either a solid color, or large, stark bars.
If you have a large difference in radii and are working in a small range, you require a large bias for
convergence. In such cases, you will get many, very small dots with little correlation wide-spread. If the
difference is very small and the values are low, a small bias is likely to result in similar conditions.
6
Alexander Saites
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