Time is Cyclic: Looping through iterations of life and death

John Conway, a magical genius, was a playful mathematician who died in the Covid pandemic in the US. His 'no-player never-ending' game is an elegantly simple algorithm that generates complexity from simplicity.

The game starts with a seed, and then the rules are applied with each loop of the algorithm. The rules decide whether a cell will survive by it's relationship to its neighbours: it dies if its lonely (less than two live neighbours) but also dies if its crowded (more than three live neighbours). It can also re-animated, lazarus style, if it has exactly three neighbours.

This week I used template python code to explore the wonders of the game of life, and took it a bit darker. You see, time is cyclic, I moved into my current home in late winter last year: now as I once again watch my neighbouring cherry blossom tree get ready to blossom, I am alerted to the aniversary of my arrival. Even the game of life is cyclic, each iteration applying the same rules, again and again. And yet the template algorithm doesn't cycle in a satisfying manner, the cells grow and die until an arbitrary end date when there is a harsh transition to the starting cycle.

As I played with the rules I began to understand a little more of Conway's world building. I increased the number of neighbours that make a cell over-crowded to four which gave a more satisfying visual of the cellular growth and dieback. I tried to represent the cycle of life, in this world life begets life , by feeding the final loop back into the algorithm as the seed, this is the animation at the top of this page.

After many iterations of no change, breaking the program and ugly loops, I landed on a satisfying looping animation by killing off cells based on the number of neighbours:  these cells died off over a shorter number of loops until there were none, this is the animation back at the top of the starting page.