Assignment 2
PART 1: SIMULATING THE SHELLING CELLULAR AUTOMATA MODEL
Create a new global variable called “unhappy-ratio” that is calculated as the percentage of unhappy cells divided by the percentage of similar cells. Create a plot that displays the unhappy-ratio variable at each time step.
DISCUSSION
1 What minimum level of self-preference leads to emergent patterns of segregation?
minimal level leading to emergent pattern of segregation is 21% (%-similar-wanted, A).
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the 20% level (A) doesn't lead to emergent pattern. The turtles are just moving following their preferences but they are not creating a really emerging pattern. The % of similars in their vicinity don't exceed 60%.
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the 21% level (B) leads to emergent pattern of segregation. The % of similars in their vicinity exceeds 60%.
A) %-similar-wanted: 20%, ticks: 3, number: 2000
B) %-similar-wanted: 21%, ticks: 8, number: 2000
Resulting pattern:
Resulting pattern:
Does a specific threshold level exist that tips the system into an unstable state?
yes, for the n=200 the threshold exist as 80 - 81% of 5-similar-wanted.
5-similar-wanted: 80%
ticks: 971
number: 2000
2 Does a specific threshold level exist that tips the system into an unstable state?
Yes, if %-similar-wanted is 81 % (C, ticks: -, number: 2000), plots are showing the no-changing self-preference values over time, thei are horizontal
If %-similar-wanted is 80% (D), still the emergent pattern could be created in longer time (about 7000 ticks), formating huge areas of similars turtles. Plots are showing increasing and decreasing number of happy and unhappy turtles overtime.
C) %-similar-wanted: 81%, ticks: -, number: 2000
D) %-similar-wanted: 80%, ticks: 7636, number: 2000 (the turtle with no neighbors is considered as happy)
3 How does increasing levels of self-preference change the nature of segregation patterns that emerge?
Increasing self-preference, the more remarquable clusters are created - more spatially extend and more aggregated. However, the time needed to increase clusters is increasing.
 %-similar-wanted: 30 %-similar: 74 |
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 %-similar-wanted: 40 %-similar: 80 |
 %-similar-wanted: 50 %-similar: 89 |
 %-similar-wanted: 60 %-similar: 89 |
 %-similar-wanted: 70 %-similar: 99 |
 %-similar-wanted: 80 %-similar: 100 |
Figure: Changing emergent pattern with increasing level of self-preference (30,40,50,60,70,80%) and final number of %-similar-wanted (74, 80, 89,96, 99 and 100% respectivelly)
4 What does the change in the unhappy-ratio at each time step tell you about the relationship between self-preference and the number of similar neighbors in one’s neighborhood?
Unhappy_ratio is reflecting global characteristics of percentage of unhappy celles divided by the percentage of similar cells so it is not directly reflecting one turtle's neighborhood but mean of the ([similar-nearby] does). However, 'unhappy' reflect state of the cell, the 'similar' reflect ste of their neighbourhood. The lower unhappy_ratio is, the more similar cells are neighborhood of 1 turtle.
If %-similar-wanted is low (30%, right) the percentage of unhappy turtles is small 9%. The percentage of unhappy turtles increases with %-similar wanted (80%, left), the % of unhappy is higher (65.4%).
The "unhappy-ratio" tell us about the ratio between "similar-wanted" and "unhappy". If the 'similar wanted' increase, the part of the unhappy turtles increase. In several time steps (if the %-similar-wanted is in range 21-80%) the number will decrease because of growing number of happy turtles until reaching 0 value. The case is similar with 80% similar wanted.
Figure: Changing pertantage of unhappy turtles in different levels of %-similar-wanted. Left: low %-similar-wanted, so low % of unhappy turtles. Segregation is established in few time-steps. Unhappy-ratio is decreasing, the neighbors of one turtles are more similar. Right: high %-similar-wanted, so high % of unhappy turtles. Segregation is established in few time-steps. The lower unhappy_ratio is, the more similar cells are neighborhood of 1 turtle
5 What general conclusions can be drawn from your answers to questions (i) to (iii)?
existence of the thresholds in agent behaviour leading to creation to
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no-pattern (self-preference 0-20%)
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emergent pattern (self-preference 21-80%)
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unstable system (self-preference 81-100%)
with increasing level of self-preferences the bigger and spatially more extent clusters of similar cells are created (2D)
cells which are isolated (total-nerby = 0) are considered to be 'happy' because of
happy? similar-nearby >= ( %-similar-wanted * total-nearby / 100 )