Home
Help
Resources
Extensions
FAQ
NetLogo Publications
Donate

Models:
Library
Community
Modeling Commons

Beginners Interactive NetLogo Dictionary (BIND)
NetLogo Dictionary

User Manuals:
Web
Printable
Chinese
Czech
Farsi / Persian
Japanese
Spanish

## NetLogo Models Library:3D/Sample Models

 Note: If you download the NetLogo application, every model in the Models Library is included.

## WHAT IS IT?

This program is an example of a three-dimensional cellular automaton, it is a 3D version of the Life model. A cellular automaton is a computational machine that performs actions based on certain rules. It can be thought of as a world which is divided into cubic cells. 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.

This particular cellular automaton is called The Game of Life. The rules of the game are as follows. Each cell checks the state of itself and its twenty-six surrounding neighbors and then sets itself to either alive or dead.

If an empty cell has n living neighbors, and r1 <= n <= r2, the cell becomes alive. If an alive cell has n living neighbors and n < r3 or n > r4, the cell dies. This is done in parallel and continues forever.

## 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.

R1, R2, R3, and R4 determine the rules of the world.

## THINGS TO NOTICE

Find some objects that are alive, but motionless.

## THINGS TO TRY

Are there any recurring shapes? What happens when you change the rules?

## EXTENDING THE MODEL

Give some different rules to the cells and see what happens.

Experiment with using `neighbors6` instead of `neighbors3d` (see below).

## NETLOGO FEATURES

The `neighbors3d` primitive returns the agentset of the patches to the north, south, east, west, northeast, northwest, southeast, and southwest as well as up, down, up-north, down-north, up-south, down-south, up-east, and so on. So `count neighbors3d with [pcolor = red]` counts how many of those twenty-six patches have the `living?` patch variable set to true.

`neighbors6` is like `neighbors` but only uses the patches to the north, south, east, west, up and down. Some cellular automata, like this one, are defined using the 26-neighbors rule, others the 6-neighbors.

## RELATED MODELS

Life - 2D version of this model Life Turtle-Based - same as this, but implemented using turtles instead of patches, for a more attractive display in the graphics window 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.

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:

Please cite the NetLogo software as: