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 Download If clicking does not initiate a download, try right clicking or control clicking and choosing "Save" or "Download".Try It in NetLogo Web

## WHAT IS IT?

The model replicates the Conway's Game of Life, a landmark contribute to the field of Applied Mathematics. In particular, its presets allow to replicate famous initial shapes of the model dynamics.

## HOW IT WORKS

Each cell (i.e., "patch" in the NetLogo Language) can be either alive (black) or dead (white). The colours are inverted if "night-mode" is on. The dynamics of the cells are described by the following three rules:
- an alive cell dies if, its surroundings, there are less than two alive neighbours (death from isolation) or more than three alive neighbours (death from overcrowding);
- it follows that an alive cell remains as such only if there are two or three alive neighbours in its surroundings;
- a dead cell becomes alive if there are exactly three alive cells in its neighbourhood.
By means of these laws of motion, it is possible to produce structures which are chaotic, in the sense that they are very sensible to initial conditions.
If the sierpinski option is selected, then a new rule is added:
- a dead cell becomes alive is the cell above it is alive.
If this rule is on and the sierpinksi shape is selected, then it is possible to witness the emergence of the Sierpinski triangle within the Game of Life (fractal within fractal!).

## HOW TO USE IT

The initial setting of the world is "wrapped horizontally", which avoids the problems induced by the torus initial setting. The model comes with different initial patterns available at the Pattern chooser, which collects some of the most famous shapes and incorporates also a random starting condition. The night-mode shifts the color scheme of the interface. The zoom slider varies the size of the patches and adapts the size of the model, in order to better appreciate its dynamics. While holding draw-cells it is possible to add now cells to the simulation or to delete them by either clicking on empty spots or on alive cells. In the end, the graph shows for each tick how many cells are alive.

## THINGS TO NOTICE

The main thing to notice is how dependent is the structure from the initial conditions: try to change some of the initial coordinates and see what happens. It is possible to do the same by emptying the interface through the relative command or by selecting the "Empty" Pattern and then add the cell with draw-cells held down.
Still, the random starting condition, once collapsed to an equilibrium, depicts some of the previously shown shapes. Try to recognize some of them and to understand why do they pop up in this context.

## EXTENDING THE MODEL

The model can fit as many new shapes as it is possible to imagine, since the Go procedure is independent of the SETUP setting. A natural expansion of the model can come with the inclusion of other starting shapes.

## RELATED MODELS

The NetLogo Library already includes a Game of Life simulation, but just for a random initial shape.

## CREDITS AND REFERENCES

The model have been adapted from LifeWiki: https://conwaylife.com/wiki/Main_Page.
I personally thanks SpicyMelon for its YouTube video on Sierpinski Triangle in the Game of Life. Your video has inspired me to believe that fractal geometry will remain always an open field of inquiry.