# Night & Day CA

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for info go here: http://en.wikipedia.org/wiki/Day_%26_Night

## WHAT IS IT?

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 block 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.

If you want to draw your own pattern, use the DRAW-CELLS button and then use the mouse to "draw" and "erase" in the view.

## 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. So `count neighbors with [living?]` counts how many of those eight patches have the `living?` patch variable set to true.

`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 Turtle-Based --- same as this, but implemented using turtles instead of patches, for a more attractive display

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 in an academic publication, we ask that you include these citations for the model itself and for the NetLogo software:

- Wilensky, U. (1998). NetLogo Life model. http://ccl.northwestern.edu/netlogo/models/Life. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

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

In other publications, please use:

- Copyright 1998 Uri Wilensky. All rights reserved. See http://ccl.northwestern.edu/netlogo/models/Life for terms of use.

## COPYRIGHT NOTICE

Copyright 1998 Uri Wilensky. All rights reserved.

Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed:

a) this copyright notice is included.

b) this model will not be redistributed for profit without permission from Uri Wilensky. Contact Uri Wilensky for appropriate licenses for redistribution for profit.

This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.

This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2001.

## Comments and Questions

patches-own [ living? ;; indicates if the cell is living live-neighbors ;; counts how many neighboring cells are alive ] to setup-blank clear-all ask patches [ cell-death ] reset-ticks end to setup-random clear-all ask patches [ ifelse random-float 100.0 < initial-density [ cell-birth ] [ cell-death ] ] reset-ticks end to cell-birth set living? true set pcolor fgcolor end to cell-death set living? false set pcolor bgcolor end to go ask patches [ set live-neighbors count neighbors with [living?] ] ;; Starting a new "ask patches" here ensures that all the patches ;; finish executing the first ask before any of them start executing ;; the second ask. This keeps all the patches in synch with each other, ;; so the births and deaths at each generation all happen in lockstep. ask patches [ ifelse (not living?) and (member? live-neighbors [3 6 7 8]) [ cell-birth ] [ if (living?) and (member? live-neighbors [0 1 2 5]) [ cell-death ] ] ] tick end to invert ask patches [ ifelse living? [cell-death] [cell-birth] ] end to draw-cells let erasing? [living?] of patch mouse-xcor mouse-ycor while [mouse-down?] [ ask patch mouse-xcor mouse-ycor [ ifelse erasing? [ cell-death ] [ cell-birth ] ] display ] end ; Copyright 1998 Uri Wilensky. All rights reserved. ; The full copyright notice is in the Info tab.

There is only one version of this model, created almost 13 years ago by David Weintrop.

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