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Evolution of Rules in Conway's Game of Life: Genetic Algorithm Exploration

Dive into the world of cellular automata with a focus on modifying the classic Conway's Game of Life rules using a Genetic Algorithm approach. Explore how changing neighbor cell conditions affect the evolution of patterns. Experiment with fitness functions and genetic operations to discover intriguing rule variations.

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Evolution of Rules in Conway's Game of Life: Genetic Algorithm Exploration

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  1. Game of Life Changhyo Yu 2003. 06. 09

  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 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 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 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. Game of Life

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