Game of life

The game of life, with a random element

We can study the complexity of a simpler system to understand how complexity works in our universe. We will study the cellular automata "Advanced game of life".

The "normal game of life", first popularized by John Conway, is a cellular automata that consists of a grid of cells which follows rules to determine if a cell is on or off.

The rules are:

Count our neighbors from the previous step,

a cell with 1 or less neighbors will turn off ("die due to starvation")
a cell with 2 or 3 neighbors it will stay on if it is on already
a cell with 3 neighbors will turn on if it is off
a cell with 4 or more neighbors will turn off ("die due to overpopulation")

Some external sites have a working java program where you can play with the game of life:

A java version of life.
Another java version (in case the above link is down)

A game of life will create many interesting patterns and patterns of cell motion as it evolves through time.

Notice that the initial configuration of the normal game of life is what creates the interesting behavior. The initial configuration creates a cascading series of events, which eventually runs down into some repeating patterns or a static image.

Each stage of the normal game of life is completely determined by the previous time step. The complexity of a normal game of life does not change because of this, for the probability of any particular configuration is 100%, given initial conditions.

The complexity of any normal game of life does not change.

Our advanced game of life is the same as the normal game of life, except with the addition:

between every step of the cellular automata, each stage has a 5% chance of automatically changing state (from on to off, or off to on).

In this universe, we can begin with no information, a completely blank universe. Then as time passes, the universe can move into less probable states. Most less probable states will be rapidly erased when a single cell turns on. But when multiple cells turn on near each other, they can create persisting complexity as they all reinforce one another to stay around. These persitent islands can be eliminated by random fluctuations around them. The persistent islands can grow into even more complex phenomena by chance as well.

To the universe complexity page