15 days I wrote the blog “yet another blog about the “Conway’s Game of Life” . My purpose was convincing you that very simple individual rules could produce group patterns. This patterns emerge from the individuals interacting with their environment and nothing else.

I promised I was letting the best for today. So here it is. You probable were wondering how complex this group patterns could get with the right positioning. Actually what I showed in the previous blog were just the most basic and well known examples.  There are much more complex things. Take a look at the next youtube video, but start it at minute 1:10, since you don’t need explanations about the game of life anymore.

[youtube vgICfQawE]

 

That is very cool but there is more. Some very simple patterns can produce very unstable sequences (chaotic) structures. You can go here and click on run. It takes 5206 to converge (Here is a list of other long-lived patterns that you may want to try). Of course you can also randomize the canvas and wait. It could easily happen that you stare at your screen for a few days, weeks. What to say? The universe is still here in a constant accumulation of simple interaction of small particles.  Even in a simple game like this would be almost (just giving a benefit of doubt) impossible to predict the final stage, and we are starting just five individuals.

You may say, simply run the game and then you have your prediction. First, is that really a prediction? Second, there is a practical problem if you want to apply that to, say, the universe. You need another one to simulate it (and a faster one so you can use the prediction). There is another solution. Simplify the individuals. Instead of simulating a whole human being, just grab the main characteristic of his behaviour and you may learn something of the factors you picked it up. This is the theoretical background of my thesis and I will be talking about this in many different ways.

But let’s go back to the “Conway’s Game of Life” to stress two important things:

  1. Actually the “Conway’s Game of Life” is a more complicated version of something even more simple that produce complex patterns. It is just another example of a Cellular Automata. Don’t worry, my next blog is going to be about it. For now, I am just going to add that the “Conway’s Game of Life” is a 2 dimensional games. The simplest cellular automata has just 1 dimension, and still produces chaos
  2. The “Conway’s Game of Life” has the same computational power as a universal Turing machine.  I don’t know if I will be talking about the Turing machine at some but, for now, just consider that this game is “as powerful as any computer with unlimited memory and no time constraints: it is Turing complete”[1].

Three important conclusions so far:

  1. The initial conditions (patterns) determine dramatically the ending result.
  2. Chaos could come me from very simple conditions. That is to say, you don’t need complicated models to get interesting environments. You are going to find head aching problems even in the restrictive and conditioned environment of math.
  3. The predictability inside chaos is still possible. You just need another universe :D. Here, I am very satisfied and assert that chaos is different randomness. You cannot predict the latest. The question, still open in the science, is “does randomness exist at all?”

Next entry: Cellular Automata

[1] http://en.wikipedia.org/wiki/Conway’s_Game_of_Life

Around 1970,  John Horton Conway created a fascinating game called “Life” [1].  The reason for the name is going to be quite obvious as I quote the rules of the game. Before that just imagine a large white checkboard (the world where ‘Life’ happens) and a plentiful supply of counters (the creatures that plays ‘Life’). Counters could be simple ‘poker chips’. See Figure 1. to be clear.

Figura 1. The set of the game “Life”. A checkboard with counters (the black dot) represents live individuals, the rests are dead ones.

So, how to play? In fact you (or the computer) just have to follow three rules. “Conways genetic laws are delightfully simple. First note that each cell of the checkerboard (assumed to be an infinite plane) has eight neighboring cells, four adjacent orthogonally, four adjacent diagonally. The rules are:

  1. Survivals. Every counter with two or three neighboring counters survives for the next generation.
  2. Deaths. Each counter with four or more neighbors dies (is removed) from overpopulation. Every counter with one neighbor or none dies from isolation.
  3. Births. Each empty cell adjacent to exactly three neighbors–no more, no fewer–is a birth cell. A counter is placed on it at the next move.” [1]
So the game is fairly simple and seems boring. But take a look at Table 1. Those are 10 different examples of possible words. As you can see, several group behaviours are produced with the same three Conway’s rules. The only thing that has change in each world is the initial configuration of the game. Thing of each column as small society. The first column would be examples of societies that never change (‘classic’). The second column would be cyclic societies (I would say mesoamerica is a good example or the oscillation between republicans and democrats). The third column, well, that is for sure a nomadic group.

Table 1. The table presents three kinds of examples. First column is about still lives, the world is not going to change and it doesn’t matter how many times you apply the rules. The second column is about oscillators, this worlds produces cycles of  2 or 3 periods following the same rule. The third one is about spaceships, the individuals “move”  through the grid indefinitely. (Source: Wikipedia [2])

Still lifes
BlockGame of life block with border.svg
BeehiveGame of life beehive.svg
LoafGame of life loaf.svg
BoatGame of life boat.svg
Oscillators
Blinker (period 2)Game of life blinker.gif
Toad (period 2)Game of life toad.gif
Beacon (period 2)Game of life beacon.gif
Pulsar (period 3)Game of life pulsar.gif
Spaceships
GliderGame of life animated glider.gif
Lightweight spaceship (LWSS)Game of life animated LWSS.gif
Remember, this doesn’t have a top down construction. This is build from each individual rules. It doesn’t matter that it seems a very coordinated and dictatorial group behaviour. Each cell has its own behaviour and there is no centred government. Don’t trust me? try it in a piece of paper, it is going to be just as little less boring than a Sudoku.
There is more, but this blog is already large and I feel like keeping the best part for the next post. But before going, enjoy the little example in the Figure 2. What could it be? Two little societies in a battle?
asdf
Figure 2. Glidders. This is a slightly more complex example. Also from [2].

[1] Gardner, Martin (1970-10). Mathematical Games – The fantastic combinations of John Conway’ new solitaire game “life”223. pp. 120–123. ISBN 0-89454-001-7. Archived fromthe original on 2009-06-03. Retrieved 2011-06-26.

[2] http://en.wikipedia.org/wiki/Conway’s_Game_of_Life