Description of Life

• Played on an infinite 2d grid of cells • Each cell has 8 neighbors • Each cell is either Live or Dead • The 2d grid starts off with a seed of 1 or more live cells. Description of Life • The rules of the game of life are: – A Live cell dies if it has fewer than 2 live neighbors. (UNDER POPULATION) – A Live cell dies if it has more than 3 live neighbors. (OVER CROWDING) – A Live cell remains alive if it has 2 or 3 live neighbors. (SURVIVAL) – A Dead cell becomes Live if it has exactly 3 live neighbors. (BIRTH) Description of Life • All four rules are implemented simultaneously and result in a new instance of the grid (the next generation.) A few examples:--> (2 die, 0 born) (3 survive, 1 born, 0 die)--> What happens in next generation? (1 survives(center), 2 born, 2 die)--> What happens in next generation? Description of Life • It is easy to see that many seed states result in, after some number of generations, a steady state of zero or more live cells that do not change in further generations. • Conway had a conjecture early on that “no pattern can grow without limit ” and he offered a prize to readers of a Martin Gardner column in Scientific American to the first person who can prove or disprove the conjecture before the end of the year (1970). • Let's see some interesting examples of life played out. Life • Among other things, it is very interesting that the Game of Life, with such simple rules, is as powerful as