Conway's Game of Love

Mathematician John Conway loved playing games. He also loved using math to invent games, the best known of which is his Game of Life. Not the Hasbro board game, but rather a game based on simple mathematical rules that simulates the life and death of simple organisms.

Since its Valentine’s Day, we thought we’d take inspiration from Conway’s Game of Life by playing the game in a way that he might have done. We drew the outline of a heart on the Game of Life grid, much like the one on the left hand side of our featured image, and let the game play out to see what patterns might emerge from that starting design. We next drew another heart, the same size as the first one, but this time, filling in the inside of the heart.

But before we clicked the button to “start reproducing”, we wondered how that simple difference might change the outcome of the game. Would the filled-in heart produce similar patterns to the simple outline of a heart? Would it “live” longer, or rather, would it go through more generations than the outlined heart before it might either stagnate (reach a pattern that doesn’t significantly change) or die out (disappear altogether)?

We’re not going to tell you the outcome, because it’s easier to find out for yourself. Draw your own heart in the grid below by clicking the squares to make it, then click the “start reproducing” button to bring it to life. Then try again with a variation of your first heart design. If you’re accessing this article on a site that republishes our RSS news feed, please click through to our site to access a working version.

Click on table cells to toggle the cells as alive or dead.

We will say we were surprised by the symmetry in the patterns that emerged from our initial hearts. If you play the game again, you might try making your heart design a little different. Would the outcomes change if you made it bigger or smaller? What would happen if you only filled in half of the heart? Would that live longer or shorter than your previous longest-lasting initial heart design? What would change if you made that design asymmetric? Is it possible to tweak your heart design to make its descendant patterns stay alive forever?

We don’t know the answers to any of those questions. Yet. The best way to find out is to play. Have fun and a happy Valentine’s Day!

Previously on Political Calculations

• John Conway’s Game of Life
• Omniperiodic Oscillators in the Game of Life
• A Game About Love and Graphing
• A Formula for Love
• The 37 Percent Solution
• The Maths of Love
• Math Formula Explains Geek’s Dating Drought