20260502-1716-conway-s-game-of-life---programmatic-rules-and-par

Conway’s Game of Life - programmatic rules and parameters

Answer

Conway’s Game of Life is a zero-player cellular automaton operating on an infinite 2D grid where each cell is either alive or dead. All state transitions are governed by exactly 4 deterministic rules applied simultaneously to every cell each generation, based solely on each cell’s 8 Moore neighbors (horizontally, vertically, and diagonally adjacent cells).

Key Findings

• Rule 1 - Underpopulation: Any live cell with fewer than 2 live neighbors dies

• Rule 2 - Survival: Any live cell with 2 or 3 live neighbors lives to the next generation

• Rule 3 - Overpopulation: Any live cell with more than 3 live neighbors dies

• Rule 4 - Reproduction: Any dead cell with exactly 3 live neighbors becomes alive

• Core parameters: infinite 2D orthogonal grid, binary cell states (alive/dead), Moore neighborhood (8 adjacent cells), synchronous updates per tick

• Minimal C++ implementation: uses a 2D array for cell state and a parallel neighbor-count array; iterate neighbors for each live cell, then apply rules to produce next generation. Python implementations follow same logic. Grid can be finite (bounded) or infinite (sparse hash map) depending on implementation needs

Open Questions

• What are the most computationally efficient algorithms for large-scale Game of Life simulations (e.g., Hashlife algorithm vs. naive array iteration) and at what grid sizes do they matter?

• What variant rule sets exist (e.g., HighLife, Day & Night, Seeds) and how do their survival/birth conditions differ from the standard B3/S23 notation used in Conway’s original rules?

Entities

john-horton-conway achim-flammenkamp bill-gosper stephen-a—silver edwin-martin alexander-tokarev playgameoflife-com conwaylife-com real-python rust-and-webassembly scientific-american medium numberphile study-com programming-for-lovers stephen-hawking the-guardian quanta-magazine

Concepts

cellular-automaton-grid game-of-life-rules cell-state-transitions moore-neighbourhood emergent-pattern-formation programmatic-implementation zero-player-simulation

Sources

• https://playgameoflife.com/lexicon/101

• https://study.com/learn/lesson/conways-game-of-life-overview-rules-instructions.html

• https://realpython.com/videos/conway-game-of-life/

• https://medium.com/@Sash0k/conways-game-of-life-3555ecbf4d13

• https://rustwasm.github.io/book/game-of-life/rules.html

• https://programmingforlovers.com/chapter-3-building-a-self-replicating-cellular-automaton-with-top-down-programming/chapter-3-core-text/the-game-of-life/

• https://www.youtube.com/watch?v=jGTCwCLRCrE

• https://p5js.org/examples/math-and-physics-game-of-life/

• https://jonoshields.com/post/cellular-automata-tutorial/

• https://www.instructables.com/Cellular-Automata-and-an-Implementation-of-Conways/

• https://github.com/mwharrisjr/Game-of-Life

• https://github.com/shiffman/ConwaysGameOfLife

• https://github.com/Tugamer89/GameOfLife

• https://github.com/erikrose/conway

• https://github.com/lkwilson/Conways-Game-Of-Life-AI

• https://medium.com/@theyordanos/implementing-conways-game-of-life-in-c-e80f4448cd89

• https://www.geeksforgeeks.org/dsa/conways-game-life-python-implementation/

• https://stackoverflow.com/questions/26963533/john-conways-game-of-life-basic-implementation-in-c

• https://realpython.com/conway-game-of-life-python/

• https://github.com/Dor-sketch/game-of-life-ai

• https://www.reddit.com/r/math/comments/3vxphq/have_alternatives_to_conways_game_of_life_link_in/

• https://www.reddit.com/r/cellular_automata/comments/r9ti9j/any_game_of_life_explore_an_infinite_set_of_rules/

• https://www.reddit.com/r/askscience/comments/34t6gd/could_a_cellular_automatonlike_conways_game_of/

• https://www.reddit.com/r/indiegames/comments/1f1dqq8/im_developing_a_game_where_you_fight_cellular/

• https://www.reddit.com/r/cellular_automata/rising/