Game of Life

Changhyo Yu2003. 06. 09

Game of Life 2

Introduction Conway’s Game of Life

Rule Dies if # of alive neighbor cells =< 2 (loneliness) Dies if # of alive neighbor cells >= 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 3^9 = 19683

Game of Life 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 } => same as conway’s

Way to find a new rule To acquire the wanted interestingness, use G.A.

Game of Life 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 generation’s live cells

Game of Life 5

Genetic Algorithm Main routine

while(generation<MAXGENS) {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

Game of Life 6

Genetic Algorithm – cont. Variables

Rules[0] ~ [8] = { 0 1 0 0 2 0 0 1 0 }; Rule has any possible choices of 3^9

Fitness (1) The variation of live cells

Find a interesting variation : 22.5

1 0 1

0 1 0

1 0 0

7 8 9

4 5 6

1 2 3

0 0 1

0 0 0

1 1 1

7 8 9

4 5 6

1 2 3

Diff_a = 1x1 + 5x1 + 7x1 + 9x1=> 22

Diff_b = 1x1 + 2x1 + 3x1 + 9x1=> 15

Game of Life 7

Genetic Algorithm – cont. Fitness

(2) The wanted number of live cells Difference =

|Init_num_of_live_cells – current_num_of_live_cells|

Fitness = factor1 x fitness1 + factor2 x fitness2

Game of Life 8

Result ( example at 100 generations )

Log files during the simulationRules 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

Game of Life 9

Conclusion I made a method to find an interesting rule

by using G.A. But, I can’t 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.