Game of Life

1
Game of Life

• Changhyo Yu
• 2003. 06. 09

2
Introduction

• Conways Game of Life
• Rule
• Dies if of alive neighbor cells lt 2
  (loneliness)
• Dies if of alive neighbor cells gt 5
  (overcrowding)
• Lives if of alive neighbor cells 3
  (procreation)
• Remains if of alive neighbor cells 4
• Possible rules to program the Game of Life
• 39 19683

3
Modified Game of Life

• New rules
• Dies if of alive neighbor cells a, b, c,
  
• Lives if of alive neighbor cells a, b,
  c,
• Remains if of alive neighbor cells a,
  b, c,
• Ex). Rules 001200000 gt same as conways
• Way to find a new rule
• To acquire the wanted interestingness, use G.A.

4
Modified Game of Life cont.

• Interestingness
• Actively changing with each generation
• The wanted number of live cells
• The fitness function of interestingness
• Fitness1 The change in the 3x3 window
• Fitness2 The difference between the current
  live cells and next generations live cells

5
Genetic Algorithm

• Main routine
• while(generationltMAXGENS)
• select()
• crossover()
• mutate()
• evaluate()
• elitist()
• Population size 25
• Generation number 50
• Probability of crossover 0.25
• Probability of mutation 0.01
• Evaluation number 100 generations

6
Genetic Algorithm cont.

• Variables
• Rules0 8 0 1 0 0 2 0 0 1 0
• Rule has any possible choices of 39
• Fitness
• (1) The variation of live cells
• Find a interesting variation 22.5

7
Genetic Algorithm cont.

• Fitness
• (2) The wanted number of live cells
• Difference
• Init_num_of_live_cells current_num_of_live_cell
  s
• Fitness factor1 x fitness1 factor2 x fitness2

8
Result ( example at 100 generations )

• Log files during the simulation
• Rules Generation Best
  Average Standard
• 0 - 8 number value fitness
  deviation
• 0 0 1 2 1 0 0 2 0 7 0.122640734
  0.092708531 0.000000002
• 0 0 1 2 1 0 0 2 0 8 0.122640734
  0.093905819 0.005986441
• 0 0 1 2 1 0 0 2 0 9 0.122640734
  0.095103108 0.008287852
• 0 0 1 2 1 2 0 0 0 10 0.215213906
  0.101200611 0.025732998
• Solution from the G.A.
• Best member of 1-th run
• 0 2 0 2 1 0 0 0 1
• Best fitness 0.487417219 for 100 generation

9
Conclusion

• I made a method to find an interesting rule by
  using G.A.
• But, I cant find an interesting examples because
  of the simulation time is too short to find a
  interesting result.
• To find a useful rule, I should extend the
  generation number in the G.A.