One-Dimensional Life

The game of Life was invented by the British mathematician John Conway and described in the "Mathematical Games" section of Scientific American in October 1970 and February 1971. Conway's game was two-dimensional. This one-dimensional version was published in BYTE magazine in December, 1978.

The evolution rule is based on a five-cell neighborhood, YYXYY, where the next generation of the center cell X depends on its own state and those of the four Y cells. The rule is: (1) a cell is born if it has 2 or 3 Y-neighbors alive, and (2) a living cell survives if it has 2 or 4 Y-neighbors.

My version was mentioned in Stephen Wolfram's A New Kind of Science, published in 2002 by Wolfram Media. Wolfram had a systematic classification of one-dimensional cellular automata, in which this version is (according to Wolfram) "outer totalistic code 624, with k = 2 and r = 2". Its behavior resembles his code 20 example in the book.

An initial configuration can be set in the top line of the simulator either by selecting one from the drop-down menu and then pressing "Load", or by setting individual cells with the Left/Flip/Right buttons, or the arrow keys and space bar. Loading "Input" permits entry of a binary configuration. "Bottom" continues evolution from the last line of the previous run. The selectable decimal fraction is the expected proportion of live cells for the "Random" configuration. After an initial configuration is loaded, pressing "Run" shows 60 stages of evolution (at once) on successive rows.

Although the BYTE article resulted in several contributions for initial configurations with interesting evolutions, most of those have been forgotten over the years. Readers are welcome to suggest new initial configurations to add to the menu. Long-lifespan forms are interesting. Also bigger gliders, and longer cycles. It is not known if there are unbounded forms (a glider gun?). There are no "still lifes". "Garden of Eden" configurations have no predecessor; 101 is the simplest.


1-D Life Simulator