#Game of life patterns series#
Here’s an example of a period 416 gun that constructs 60P5H2V0 spaceships using a series of timed glider collisions: Using combinations of spaceships, still lifes, oscillators, guns, and reactions between them, it’s possible to construct incredibly complex machines in Life. Here is a 3 glider synthesis of a medium-weight spaceship: 3 glider synthesis of MWSS Glider synthesis forms a large subset of known and actively studied Life reactions, and it was a critical piece of Conway’s existence proof of a self-replicating machine in Life. Glider Synthesis is a process by which Life patterns are created solely through collisions of gliders. “Reactions” are collisions of Life objects that produce useful outcomes. “Guns” are structures that produce a stream of spaceships Gosper’s glider gun was the first gun ever discovered: Gosper's glider gun Other common spaceships are the light-weight spaceship, and its siblings, the middle-weight and heavy-weight varieties: light-weight spaceship "LWSS" (period 4) middle-weight spaceship "MWSS" (period 4) heavy-weight spaceship "HWSS" (period 4) The simplest and most common spaceship (“common” here means it will often arise in the wild) is called a “glider”: glider (period 4) “Oscillators” are dynamic patterns that repeat themselves after a certain number of time steps: blinker (period 2) beacon (period 2) pulsar (period 3) pentadecathlon (period 15)Ī “Spaceship” is a type of oscillator that moves across space as it oscillates. Stable configurations, called “still lifes”, do not change over time: block loaf boat beehive In general, patterns in Life can be broken into a few broad categories, described below. Other patterns were meticulously designed by people, often built from smaller subunits with well-characterized behavior. Some patterns are readily observed in the wild – spontaneously emerging from a random soup of living and dead cells. One of the most interesting things about Life is the variety of patterns that can be constructed within it. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.Any live cell with more than three live neighbors dies, as if by overcrowding.Any live cell with two or three live neighbors lives on to the next generation.Any live cell with fewer than two live neighbors dies, as if caused by under-population.The rules of Life are loosely based on population dynamics (copied from wikipedia below): In the Game of Life, a cell’s behavior is dictated by its current state (alive or dead) and the state of its eight nearest neighbors. Though the rules that govern Life are very simple, the results can become quite complex. Now that I find myself with a lot of time on my hands, I figured I’d clean up these notes and finally kick this blog off (inaugural post!).Ĭonway’s Game of Life is a 2D cellular automaton - a simulated world set on a grid of pixels (cells). Unfortunately, John Conway passed away recently, which got me thinking about Life again (not to sound too sappy).
This post is (mostly) some notes I took back in 2015 while trying to understand how this metapixel was designed. These days you can spend a long time on YouTube exploring the seemingly impossible things people are designing in the “simple” Life universe. These investigations have resulted in a lengthy taxonomy of motifs, reactions, and mechanisms, as well as engineering principals and design abstractions. Since its inception in 1970, Conway’s Game of Life has developed a cult following of researchers, engineers, and hobbyists, pushing each other to construct increasingly elaborate “machines” from pixels on a screen. From there you could create a meta-metapixel out of metapixels and so on….Īt the time I was reading the book The Recursive Universe by William Poundstone, which gives a detailed breakdown of John Conway’s 1982 proof of self-replicating objects in Life. With a big enough matrix of these “metapixels”, you can simulate a meta-version of Life on a massive scale. The purpose of the machine is to emulate a single Life pixel. A few years ago I came across this video, showing a complex machine built entirely in Conway’s Game of Life:
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