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NetLogo Models Library:
Sample Models/Computer Science/Cellular Automata

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Life Turtle-Based

[screen shot]

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.)

## WHAT IS IT?

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 two-dimensional 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.

## HOW IT WORKS

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 arrow-headed shape, like this:

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.

## HOW TO USE IT

The INITIAL-DENSITY slider determines the initial density of cells that are alive. SETUP-RANDOM places these cells. GO-FOREVER runs the rule forever. GO-ONCE 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 DRAW-CELLS button and then use the mouse to "draw" and "erase" in the view.

CURRENT DENSITY is the percent of cells that are on.

## THINGS TO NOTICE

Find some objects that are alive, but motionless.

Is there a "critical density" - one at which all change and motion stops/eternal motion begins?

## THINGS TO TRY

Are there any recurring shapes other than gliders and blinkers?

Build some objects that don't die (using DRAW-CELLS)

How much life can the board hold and still remain motionless and unchanging? (use DRAW-CELLS)

The glider gun is a large conglomeration of cells that repeatedly spits out gliders. Find a "glider gun" (very, very difficult!).

## EXTENDING THE MODEL

Give some different rules to life and see what happens.

Experiment with using `neighbors4` instead of `neighbors` (see below).

## NETLOGO FEATURES

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 8-neighbors rule, others the 4-neighbors.

## RELATED MODELS

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 3-color 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

## CREDITS AND REFERENCES

The Game of Life was invented by John Horton Conway.

See also:

Von Neumann, J. and Burks, A. W., Eds, 1966. Theory of Self-Reproducing Automata. University of Illinois Press, Champaign, IL.

"LifeLine: A Quarterly Newsletter for Enthusiasts of John Conway's Game of Life", nos. 1-11, 1971-1973.

Martin Gardner, "Mathematical Games: The fantastic combinations of John Conway's new solitaire game `life',", Scientific American, October, 1970, pp. 120-123.

Martin Gardner, "Mathematical Games: On cellular automata, self-reproduction, the Garden of Eden, and the game `life',", Scientific American, February, 1971, pp. 112-117.

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.

## HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

* Wilensky, U. (2005). NetLogo Life Turtle-Based model. http://ccl.northwestern.edu/netlogo/models/LifeTurtle-Based. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Please cite the NetLogo software as:

* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 2005 Uri Wilensky.

![CC BY-NC-SA 3.0](http://ccl.northwestern.edu/images/creativecommons/byncsa.png)

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/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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