Game of Life

One of my heroes is John Conway, a mathematician renowned for his contributions to the theory of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. Sadly, Conway’s life was cut short in 2020 due to complications related to COVID-19. He is probably most famous for devising the Game of Life, a Turing-complete simulation that not only showcased the potential of cellular automata but also sparked widespread interest in this field. This simulation raises some interesting philosophical issues about the nature of patterns, emergent behavior, and artificial intelligence.

I have paid tribute to Conway’s legacy by recreating the Game of Life within a single HTML file, incorporating CSS and JavaScript. Please give it a try in your web browser and also right click to check out the source code!

About The Game of Life

The Game of Life, also known simply as Life, is not a game in the traditional sense but a cellular automaton devised by the British mathematician John Horton Conway in 1970. This fascinating creation is a zero-player game, meaning its evolution is determined by its initial state (or ‘seed’), requiring no further input from human players. Life is played out on a grid of square cells, each of which can be in one of two possible states: alive or dead. Every cell interacts with its eight neighbors, which are the cells that are horizontally, vertically, or diagonally adjacent.

Rules of the Game

The rules of Life are simple but lead to an extraordinary range of potential outcomes:

  • Birth: A dead cell with exactly three live neighbors becomes a live cell (as if by reproduction).
  • Survival: A live cell with two or three live neighbors stays alive for the next generation.
  • Death: In all other cases, a cell dies or remains dead (due to overpopulation or loneliness).

History and Impact

Since its inception, the Game of Life has attracted considerable interest because of the surprising ways in which the patterns can evolve. It has connections to various areas of mathematical research, including systems theory, computer science, and theoretical biology. Life’s popularity was boosted by its coverage in Martin Gardner’s column in the October 1970 issue of Scientific American magazine. It is known for helping to bring the concepts of cellular automata to the attention of a wider audience.

Philosophical and Educational Implications

The Game of Life serves as a powerful illustration of how complex patterns and behaviors can emerge from simple rules. It’s a metaphor for the unpredictability and intricacy of life itself. In educational settings, it’s used to teach students about emergent behaviors, simulation, and mathematical concepts. Philosophically, it challenges our understanding of “life” and “intelligence” in a simulated environment and raises intriguing questions about the nature of life and the universe. It subtly echoes the idea that simple laws, followed rigorously, can lead to complex and unforeseen outcomes, much like the universe we live in.

Conclusion

The Game of Life stands as a testament to the beauty of mathematics and the fascinating complexities of emergent systems. It encourages exploration and experimentation, offering a boundless playground for both the curious and the scholarly. Whether used as a teaching tool or pondered as a philosophical artifact, Life continues to captivate and inspire, transcending the boundaries of science and art.