Game of life and death

It was sad to learn earlier of the death of John Conway, the mathematician behind the Game of Life.

John Horton Conway, a ‘magical genius’ in math, dies at 82The New York Times
During what Dr. Conway called his “annus mirabilis,” roughly 1969 to 1970, he discovered what’s known as the Conway group, an entity in the realm of mathematical symmetry that inhabits 24-dimensional space. He discovered a new type of number, “surreal numbers.” And he invented the cellular automaton Game of Life, which is among the most beautiful mathematical models of computation. He described it as a “no-player never-ending” game.

I first came across this strange no-player game some time ago, and was struck by how simple its rules were, yet how intricate the patterns could become.

John Conway’s Game of Life
Each cell with one or no neighbors dies, as if by solitude.
Each cell with four or more neighbors dies, as if by overpopulation.
Each cell with two or three neighbors survives.
Each cell with three neighbors becomes populated.

game-of-life-and-death
I knew that these simple rules could create many different kinds of structures…

John Conway, inventor of the Game of Life, has died of COVID-19Ars Technica
This video, for example, shows a gun that consists of several large structures that each generates irregular streams of gliders. A bunch of gliders—37 to be exact—collide with one another in just the right way to produce a complex spaceship called a 6-engine Cordership, which then proceeds in another direction. It takes 784 moves to produce a Cordership before the cycle repeats.

… but I hadn’t appreciated just how complex they could get.

First replicating creature spawned in life simulatorNew Scientist
When Wade posted his self-replicating mathematical organism on a Life community website on 18 May, it sparked a wave of excitement. “This is truly ground-breaking work,” wrote a fellow Life enthusiast, Adam Goucher, on the website Game of Life News. “In fact, this is arguably the single most impressive and important pattern ever devised.”

My understanding of all this stops way before these videos.

I can follow along well enough to make one of those glider guns, but a digital clock? You’re kidding me.

How’s this for meta? The game of life built within the game of life. No clue what’s going on here.

Let’s leave the last word to the man himself.

Stable_puffer_animation