EXPLORABLES

This explorable illustrates one of the most famous complex dynamical systems: **The Game of Life** developed by John Horton Conway in 1970. The *Game of Life* is a simple, discrete time dynamical
system that evolves on a square lattice. Lattice cells can be **alive** or **dead**, interact with their neighboring cells, and evolve according to simple rules that mimic natural processes of **replication**, **competition** and **cooperation**.

Although the dynamic rules are very simple, the *Game of Life* can generate a wide range of dynamic patterns: spatio-temporal chaos, periodicity, self-replicating structures, and many other emergent phenomena. It plays an important role in biology, social sciences, physics, and the theory of computation.

* Press Play* and keep on reading ….

## This is how it works

The *Game of Life* is a cellular automaton. It evolves on a two dimensional, square lattice. Each lattice cell has a binary state variable, 1 or 0, representing alive or dead, respectively. In the display panel * live cells are black*, and

*. Each cell interacts with its 8 nearest neighbors. The states of all cells are updated synchronously and depending on the states of each cell’s neighboring cells.*

**dead cells are white**### The rules are very simple:

- If a cell is alive and
**has less than 2 alive**neighbors it will**die**. - If a cell is alive and
**has more than 3 alive**neighbors it will also**die**. - If a cell is alive and has
**2 or 3 alive neighbors**it will continue to**live**. - A dead cell will
**become alive**in the next step if it has**exactly 3**alive neighbors.

The first three rules imply that only when the number of neighbors is suitable, namely 2 or 3, a cell can survive. Overpopulation or too much competition will kill a cell (rule 2). Underpopulation, the lack of required cooperation, will also kill a cell (rule 1). Rule 4 mimics reproduction: Alive cells in the neighborhood can have a baby in the center.

So, in a nutshell, these simple rules mimic three vital biological forces, **cooperation**, **competition** and **reproduction**.

## Inititial conditions

The above * rules are static*, no parameters are involved. However,

*, the*

**depending on the initial conditions***Game of Life*generates different classes of patterns.

### Chaotic patterns

By default the initial setup is random, each cell is assigned its state randomly. With the * density slider you can control the initial fraction* of alive and dead cells. In this scenario you will observe that very quickly a dynamic pattern will emerge that exhibits little patches that are static and other regions that are highly dynamic. If you look closely, you will see that every now and then

*are generated that move diagonally until they collide with other parts of the pattern.*

**little gliders**### Gliders

If you * select the tiny glider* setup in the control panel you can inspect how a tiny glider works in detail. The pattern is such that the glider moves constantly into one direction. Without any obstacles, this will go on forever. If you select

*, you can observe what happens if these critters collide.*

**tiny glider swarm**There are countless * other glider forms*, or

*: Patterns that move in one direction, despite the fact that nothing in the rules would indicate that.*

**spaceships**### Glider guns

An interesting feature about the *Game of Life* is its capacity to host replicating patterns. In the control panel you can choose three different patterns that generate gliders, known as * gliders guns*. Some of these can be very complex.

### Pulsars

One can also find initial conditions for periodic patterns that repeat after a certain number of iterations. Some of these * pulsars* are really complex as the example shown here. If you are patient you can see in the example how a structure in the center is built up and gets removed again, periodically.

## Further reading

The *Game of Life* has practically no limit in terms of the complexity of patterns it can generate. A great source for exploring this further is **Golly**, an internative Game of Life simulator. Golly also offers different versions and variations of the *Game of Life* slight variations of the original rules.

It’s also worthwhile to whatch **this youtube video on the Game of Life**.