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Day and Night

by Abhishek Bhatia (Submitted: 06/26/2014)

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## WHAT IS IT?

This program models a two-dimensional cellular automaton. This particular cellular automaton is called Day and Night.

Cellular automata (CA) were invented in the 1940s by Stanislaw Ulam and John von Neumann to prove that self-reproduction is possible in machines and to further link biology and compuatation.

A CA is a collection of cells arranged in a grid, such that each cell changes state as a function of time according to a defined set of rules that includes the states of neighboring cells. In other words, a cellular automaton can thought of as computational machine performing actions based on specified rules. These are idealized models of complex systems as they consist of large network of simple components with limited communication among components and no central control. Cellular automata result complex dynamics from simple rules.

The rule modeled here is given the name "Day & Night" because both its states states are symmetric meaning if all states are switched if on, turn off vise versa the automata will proceed in the same manner.

As with Conway ’s Life the automaton model here displays Class IV Behavior. Although the day and night rule set is classified as a chaotic cellular automaton, it behaves very differently from Conway's original rules because of its unique properties.

## HOW IT WORKS

The day and night rule set is 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. In this cellular automaton, a living cell survives if it has 3, 4, 6, 7, or 8 neighbors and a dead cell becomes alive when it has 3, 6, 7, or 8 neighbors (otherwise, a cell remains in the same state). This is done in parallel and continues forever.
It exhibits complex behavior similar to Conway's Game of Life : there exist numerous well-known guns and small oscillators as well as spaceships formed by combining oscillators in such a way that they periodically emit spaceships of various types

## HOW TO USE IT

The INITIAL-DENSITY slider determines the initial density of cells that are alive.
SETUP-RANDOM initializes the model with a percentage of the cells alive.
The percentage alive cells is determined by the INITIAL-DENSITY slider.
GO-FOREVER runs the model with rule set forever.
GO-ONCE runs the model with rule set 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 stable shapes that are motionless. Also, notice any recurring shapes.

Observe how the population dynamics changes in each intialization and the how quickly each leads to a different stable point.

Notice how the chaotic structures gradually consdilate into large regions of living and dead cells with constantly shifting boundaries with activity which mirrors the behaviour of other regions.

Observe how the intensity of living cells affect the population dynamics in any particular simulation. Compare the same to Conway's orginal rule set. Do intializations stablize relatively quickly?

View the PERCENTAGE CURRENT DENSITY monitor to see the current value of density of living cells.

## THINGS TO TRY

Is it possible for this cellular automata to be used to compute anything? How?

Try to build various objects which don't die (using DRAW-CELLS).

Try to change the shape of grid and see how it affects the steady state as well as the time to reach it.

## EXTENDING THE MODEL

Modify the rules of the model to simulate different complex behaviours and observe the resulting character of a given rule set.

## CREDITS

The author would like to acknowledge Mr. Rinkaj Goyal, USICT for his guidance and support which has been immense help in understanding the fundamentals of Netlogo and complex systems as well as provided motivation to carry out authentic and valuable research.

## REFERENCES

e-mail: abhigenie92@gmail.com<mailto:abhigenie92@gmail.com>

Day & Night was invented and named by Nathan Thompson in 1997, and later explored and discussed by David I. Bell.

Bell, David I. (1997), Day & Night - An Interesting Variant of Life
Pete Carlton. "Pete's Game of Life Page: B3678 S34678
Variations on Conway’s Game of Life and Other Cellular Automata ,David Hua and Martin Pelikan

Life model in Netlogo library was particularly helpful for reference.

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