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NetLogo Models Library: 
If you download the NetLogo application, this model is included. (You can also run this model in your browser, but we don't recommend it; details here.) 
This model is the same as the Life model, but with a more attractive display. This display is achieved by basing the model on turtles rather than patches.
This program is an example of a twodimensional cellular automaton. This particular cellular automaton is called The Game of Life.
A cellular automaton is a computational machine that performs actions based on certain rules. It can be thought of as a board which is divided into cells (such as square cells of a checkerboard). Each cell can be either "alive" or "dead." This is called the "state" of the cell. According to specified rules, each cell will be alive or dead at the next time step.
The rules of the game are as follows. Each cell checks the state of itself and its eight surrounding neighbors and then sets itself to either alive or dead. If there are less than two alive neighbors, then the cell dies. If there are more than three alive neighbors, the cell dies. If there are 2 alive neighbors, the cell remains in the state it is in. If there are exactly three alive neighbors, the cell becomes alive. This is done in parallel and continues forever.
There are certain recurring shapes in Life, for example, the "glider" and the "blinker". The glider is composed of 5 cells which form a small arrowheaded shape, like this:
text
O
O
OOO
This glider will wiggle across the world, retaining its shape. A blinker is a group of three cells (either up and down or left and right) that rotates between horizontal and vertical orientations.
The INITIALDENSITY slider determines the initial density of cells that are alive. SETUPRANDOM places these cells. GOFOREVER runs the rule forever. GOONCE runs the rule once.
As the model runs, a small green dot indicates where a cell will be born, but is not treated as a live cell. Grey cells are cells that are about to die, but are treated as live cells.
If you want to draw your own pattern, press the DRAWCELLS button and then use the mouse to "draw" and "erase" in the view.
CURRENT DENSITY is the percent of cells that are on.
Find some objects that are alive, but motionless.
Is there a "critical density"  one at which all change and motion stops/eternal motion begins?
Are there any recurring shapes other than gliders and blinkers?
Build some objects that don't die (using DRAWCELLS)
How much life can the board hold and still remain motionless and unchanging? (use DRAWCELLS)
The glider gun is a large conglomeration of cells that repeatedly spits out gliders. Find a "glider gun" (very, very difficult!).
Give some different rules to life and see what happens.
Experiment with using neighbors4
instead of neighbors
(see below).
The neighbors
primitive returns the agentset of the patches to the north, south, east, west, northeast, northwest, southeast, and southwest.
neighbors4
is like neighbors
but only uses the patches to the north, south, east, and west. Some cellular automata, like this one, are defined using the 8neighbors rule, others the 4neighbors.
Life  same as this, but implemented using only patches, not turtles CA 1D Elementary  a model that shows all 256 possible simple 1D cellular automata CA 1D Totalistic  a model that shows all 2,187 possible 1D 3color totalistic cellular automata CA 1D Rule 30  the basic rule 30 model CA 1D Rule 30 Turtle  the basic rule 30 model implemented using turtles CA 1D Rule 90  the basic rule 90 model CA 1D Rule 110  the basic rule 110 model CA 1D Rule 250  the basic rule 250 model
The Game of Life was invented by John Horton Conway.
See also:
Von Neumann, J. and Burks, A. W., Eds, 1966. Theory of SelfReproducing Automata. University of Illinois Press, Champaign, IL.
"LifeLine: A Quarterly Newsletter for Enthusiasts of John Conway's Game of Life", nos. 111, 19711973.
Martin Gardner, "Mathematical Games: The fantastic combinations of John Conway's new solitaire game `life',", Scientific American, October, 1970, pp. 120123.
Martin Gardner, "Mathematical Games: On cellular automata, selfreproduction, the Garden of Eden, and the game `life',", Scientific American, February, 1971, pp. 112117.
Berlekamp, Conway, and Guy, Winning Ways for your Mathematical Plays, Academic Press: New York, 1982.
William Poundstone, The Recursive Universe, William Morrow: New York, 1985.
If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.
For the model itself:
Please cite the NetLogo software as:
Copyright 2005 Uri Wilensky.
This work is licensed under the Creative Commons AttributionNonCommercialShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/byncsa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.
Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.
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