In this post, you’ll read about the Game of Life and get to know the famous British mathematician John Conway. At the end, we’ll explore a fun simulation of the Game of Life modeled on revolution and political polarization.
The Game of Life—also known simply as “Life”—is a cellular automaton invented by John Conway. It’s used to study complex systems and their behavior.
In March 1970, Martin Gardner received a 12-page letter from the renowned mathematician John Conway. On page 9, there was a headline: The Game of Life. A mathematical model, a cellular automaton that evolves generation by generation—Conway would go on to spend the rest of his career working on a type of “life” that today is known as an “infinite game with no players.”
The game is simple: you start with any initial configuration of cells on a grid, and in each round, three rules are applied:
- Birth Rule: A dead (empty) cell with exactly three live neighbors comes to life.
- Death Rule: A live cell with one or zero live neighbors dies of loneliness. A live cell with four or more live neighbors dies of overpopulation.
- Survival Rule: A live cell with two or three live neighbors continues to live.
The Game of Life is used to study complex systems, the impact of small changes on outcomes, and how communities function.
One discovered pattern in the Game of Life:
Last night, while struggling with insomnia, I decided to test the Game of Life using models of revolution and political polarization.
In this model, revolutionaries are represented by live (colored) cells, while non-revolutionaries are dead (empty) cells. The live cells are divided into two political poles: red for one group, blue for the other. The grid is 70 by 70, and the revolution starts at coordinate (30, 30) with a radius of 10.
Each round follows these rules:
- For every live cell, count the total number of red and blue neighbors. If there are fewer than two, the cell dies from loneliness.
- If the total number of red and blue neighbors exceeds four, the cell dies from overpopulation.
- If a live cell has exactly two or three blue neighbors, it becomes blue. If it has two or three red neighbors, it becomes red.
- For a dead cell, if it has exactly three red and blue neighbors combined, it comes to life. If there are more blue than red, the cell becomes blue; otherwise, it becomes red.
After each round, a political polarization model is applied. The polarization level is assumed to be 0.3. In this step, about one-third of live cells randomly switch political sides—blue becomes red, and red becomes blue.
Then the revolution model is applied. The revolution is centered at (30, 30) with a strength of 10. In this stage, the Euclidean distance of each cell from the revolution center is calculated. If the result is less than or equal to the revolution strength, dead cells are revived and live cells die. Any cell that is revived in this phase has a 50% chance of turning red and a 50% chance of turning blue.
Below, you can see a sample and explore how the system behaves with different configurations, and under what conditions it reaches stability.
An interesting point is that in some configurations, political polarization among revolutionaries leads to the rapid extinction of live cells.
If you’d like to experiment further with different parameters or tweak the game logic just for fun, you can find the code here: