Conway’s Glass of Coke

A Conway Life animation by Manfredas Zabarauskas

Last year, I posted here about Conway’s Game of Life, a cellular automaton that simulates certain complex processes.

A few minutes ago, I poured a glass of Coke and noticed that the bubbles were moving in patterns that vaguely reminded me of Conway Life.  So I took a video of it with my cellphone and posted it on YouTube:

Conway’s Game of Life

A celebrated Conway Life pattern, the "Gosper Glider"

Years ago, I read a piece in The Atlantic about something demographer Thomas Schelling had figured out:  

In the 1960s he grew interested in segregated neighborhoods. It was easy in America, he noticed, to find neighborhoods that were mostly or entirely black or white, and correspondingly difficult to find neighborhoods where neither race made up more than, say, three fourths of the total. “The distribution,” he wrote in 1971, “is so U-shaped that it is virtually a choice of two extremes.” That might, of course, have been a result of widespread racism, but Schelling suspected otherwise. “I had an intuition,” he told me, “that you could get a lot more segregation than would be expected if you put people together and just let them interact.”

One day in the late 1960s, on a flight from Chicago to Boston, he found himself with nothing to read and began doodling with pencil and paper. He drew a straight line and then “populated” it with Xs and Os. Then he decreed that each X and O wanted at least two of its six nearest neighbors to be of its own kind, and he began moving them around in ways that would make more of them content with their neighborhood. “It was slow going,” he told me, “but by the time I got off the plane in Boston, I knew the results were interesting.” When he got home, he and his eldest son, a coin collector, set out copper and zinc pennies (the latter were wartime relics) on a grid that resembled a checkerboard. “We’d look around and find a penny that wanted to move and figure out where it wanted to move to,” he said. “I kept getting results that I found quite striking.”

Programming computers to play this game, Schelling found that strong residential segregation arose even if he assumed that each member of the set would stay put with only a single neighbor of the same category.  This provided evidence, not only that Schelling might be right about residential segregation, but also that social order in general can arise in ways that do not directly reflect the intentions of any particular member of that society.  All of Schelling’s virtual people wanted to live in integrated neighborhoods, yet it was precisely the actions they took to pursue that goal that inexorably led to the creation of segregated neghborhoods. 

Schelling’s tests reminded me of Conway’s Game of Life, a cellular automaton that mathematician John Conway invented in 1970.  The procedure of Conway is very similar to Schelling’s.  An indefinite number of square cells are arranged in a square grid.  Each cell is in one of two conditions, live or dead.  Each cell is in contact with eight other cells: one directly above, one directly below, one directly to the right, one directly to the left, and one on each of the four corners.  If a cell is alive, it remains alive if and only if it is in contact with two or three other live cells.  If a cell is dead, it remains dead unless it is in contact with exactly three dead cells.    Some very simple initial patterns take a surprisingly long time to stabilize in Conway Life: for example, this fellow (which Conway called the R-pentomino, though others call it the F-pentomino) goes on generating new forms for 1103 generations, and along the way produces a number of spectacular structures:

You can easily test out patterns here; some especially famous patterns are collected here and here.

Conway’s Game of Life came back to mind a couple of weeks ago, when this xkcd strip appeared:

Someone came up with a cellular automaton that could qualify as “Strip Conway’s Game of Life”:

Various commenters tried to put humans in the role of the automated cells, and tried to devise rules based on what the people around each human are wearing that would determine which clothes the human was required to remove.  It occurred to me that a more promising approach would be to have one person start by wearing a great many articles of clothing, leaving those clothes on that were touching either two or three other articles of clothing, removing those that were touching fewer than two or more than three articles of clothing, and putting clothes on bare spots that were bordered by exactly three articles of clothing.  Eventually, somebody might get naked. 

Then yesterday, Alison Bechdel announced on her blog that she’d drawn a comic for McSweeney’s magazine.  The comic represents a modified version of Milton Bradley’s board game called The Game of Life

Bechdel's Life

In the comments on that post, I brought up Conway’s Game of Life.  So, I decided the time had come to post about it here.