An Investigation of Cellular Automata

1
An Investigation of Cellular Automata

• Timmy Hunter-Kilmer
• Latimer 2/3

2
Conway's Game of Life

• Rules 23/3
• Different rules
• Inheriting from neighbors
• Mutation
• Maximum of 3 for each

3
Interpretation

• How successful are the rulesets?
• In what situations?
• Does this apply to other fields?

4
Process

• Field of 120120 cells
• Each cell has individual rules for survival
• Over many generations, one set of rules dominates
  the field
• User can see prevalence of all rules, average
  mutation rate
• User can add cells, change/view cell rules

5
Construction

• Every generation, check each cell for life/death
• Dead cells reinherit rules from neighbors, check
  based on that
• Number of cells with each rule counted
• Mutation rates averaged
• Constantly run simulation to verify changes,
  additions

6
Conclusions so far

• With one ruleset a simple pair of triplets say,
  123/234 and the other a slightly changed
  version of that say, 123/134 and sufficient
  time, the simpler ruleset will almost certainly
  cover the board.
• The results gathered in the preliminary trials
  aren't very indicative of overall
  competitiveness. For example, a ruleset that only
  occurred as the end of two trials initially could
  beat half of its opponents now.

7
Good Sets

• At this point, these are the rulesets I've seen
  most often
• 234/123 345/234 012/123
• 234/345 345/345 012/012
• 123/234
• Basically, most triplets that start fairly close
  together

8
Graphs

• Sometimes the field is clearly not going to have
  any one ruleset dominate, which is recorded as
  inconclusive.
• Occasionally two sets have had equal share on the
  board, which is recorded as a partial success,
  especially when those sets are almost identical.
• The blue bar represents complete dominance, and
  the red bar a partial share.

9
Successful Sets
10
Born rules involvement

11
Survival rules involvement