Night & Day CA

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David Weintrop (Author)

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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:

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.

Comments and Questions

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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 over 13 years ago by David Weintrop.

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