[Bonsai - Dan's Five Needle Pine] Cellular Automata ("The Game of Life")

See my new Javascript implementation of Conway's Game of Life here. Updated for 2016!

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Some oscillating/moving forms to experiment with:

Glider | Spaceship | Beacon | Clock | Toad | Blinker 3
Tumbler | Barber Shop Pole | Pinwheel | Hertz Oscillator
Big Blinker | New Blinker | New Blinker 2

First click the "Clear" button, then click on one of the above links
to enter a pattern into the grid, then click "Resume" to run it !

Examples of animated
forms that can appear:

Another simple blinker
Blinkers

Simple glider
Gliders

to milliseconds between generations.   

Source Code
Click "Get Cells" to save the state of the current generation to the text field. "Set Cells" adds the state in the text field to the grid (the contents of the text field can be copied to and pasted from other applications to save/restore a generation).

The Game of Life

First conceived by the British Mathematician John Horton Conway in 1970, "Life" was originally described as a "solitaire game" that would be played out by hand on a board with a square grid and round marker pieces. The arrival of computers with interactive graphics has made it a lot easier to view and experiment with the game.

Each change in the board is a "generation"; cells are born, live and die in each generation according to very simple rules (called Conway's "genetic laws" in the original Scientific American article):

  1. A cell with two or three neighbors lives on in the next generation.
  2. A cell with four or more neighbors dies from overcrowding.
  3. A new cell is born in any empty grid square with exactly three cells surrounding it in adjacent squares.

Despite the simplicity of the rules, the figures that emerge in a game of life can exhibit some very sophisticated behavior. Usually, groups of nearby cells increase and then disappear, seemingly boil up and evaporate as the generations roll on. But sometimes certain persistent forms emerge from the random patterns in the game. Some forms are "stable" structures that don't change between generations. Some forms are dynamic and move between two or three (or sometimes more !) shapes in an endless cycle. The most common of these is the blinker, which stays in one place and alternates between two shapes. It's common to see several stable forms and one or more blinkers left over at the end of a game of life. You might also see gliders, shapes that seem to glide across the grid, changing in cycles between three or more shapes. Every game begins with a different random dispersal of cells, so anything can happen !


Bibliography

Martin Gardner
"Mathematical Games: The fantastic combinations of John Conway's new solitaire game "life""
Scientific American, October, 1970

(also November 1970 and January, 1971)

Martin Gardner
"Mathematical Games: On cellular automata, self-reproduction, the Garden of Eden and the game "life""
Scientific American, February, 1971

Brian Hayes
"Computer Recreations"
Scientific American, vol. 249, no. 4, October, 1983

The Game of Life is very popular among computer scientists and software developers. A large number of people have devoted a lot of time to researching the growth of the patterns and developing interesting (and complex !) recurring patterns. For more information, see Tim Tyler's Cellular Automata Links page and in particular his page on Conway's Game of Life .

See also Math.com's Life Page and the Wikipedia page for Conway's Game of Life.

The Game of Life Lexicon lists a whole bunch of great starting Life patterns.


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