The field in the game of life could be finite or infinite. It is interesting to see and learn how an infinite field behaves and works.
- 17 Mar 2016
It is necessary for us to use an infinite field to make the game a little more interesting because with the size of the brick with can only display about 20x20 field which does not allow for interesting and larger experiments.
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The field, the grid, the matrix in the Game of Life can be infinite ot finite. And in this video we'll take a look at different cases for infinite and finite fields.
Let's say that we have the current case 4x4 and if we have this field 4x4,
and in this field we can ask the question: Which are the neighbours of this cell here? We are looking for the neighbours of this cell. And we can think: Ok, this cell. It has 5 neighbours. One, two, three, four, five. Because the field ends here and because the field ends here the cell does not have any more neighbours and we can consider that it has actually three dead neighbours. This, this and this. Because there are no cells here. And that's the case for a finite field. But we can also have the case of an infinite field. And for the infinite field we can say: Ok, we have this cell here and if we wrap the whole field we can say that this column here column 0 and this is column 3 this column 0 is actually right next to column 3. This here is again column 0.
So we can think of the wraping of the field of the matrix. And we can say: Ok, this cell. It has 5 neighbours one, two, three, four, five. But also it has these three neighbours. One, two, three. And this is the case for an infinite field. When we want to have the infinite field. Now the interesting question is also: What happens with the top right corner? If we have a finite field then the neighbours of this cell are actually 3. One, two, three. But if we have an infinite field, then which are the neighbours of this cell? First we have the right neighbour, but because there is no right neighbour here but the field is infinite then the right neighbour is actually this cell here. It's a neighbour. And we also have the Up neighbour and we have this neighbour here. And because there isn't a row above row 0 then we know that this is the cell that's a neighbour of our cell. That's the Up cell. And we also know that we have another cell right here. That's actually mapped as the cell here. So, this cell is this cell, this cell is this cell and this cell is this cell. And that's for infinite field. Now, the question is: Where is this neighbour and where is this neighbour? Let's think for this for a moment. If we have the Up to be this. And if we have the right to be this. Then the left should be
it's actually here.
And if we look for this neighbour. This neighbour is actully here. So this neighbour is here and this neighbour is here. And in this way we have and infinite field of about 4x4 grid and in this 4x4 we wrap both ends to that we have somehing as a sphere. And in this sphere, it's not exactly a sphere so let's not get into details but we just wrap it like this like we wrap the whole paper like this and we get an infinite field. And we wrap it again.
And that's an important thing about the field because on the brick screen as you can see we don't have that much space so we need a way to have a more complex life and for this we have an infinite field and in this infinite field we have the different cells. Let's take a look at the example.
If we now look at the program, and you can find the program below in the material section below the video and I start the new program and I select 4 rows by 4 columns and I have my grid. And in this grid, in this matrix, I would select this cell to be alive and this cell to be alive and this cell to be alive and this cell to be alive. And what we know from the explanation before is that this cell it actually currently has two living neighbours, Not two, three living neighbours. Because it has the right neighbour which should be here but it is actually here and it has the Down neighbour which should be here but because the field is infinite it is actually here. And we have the neighbour that's on a diagonal and it should be right here but it is not here it is actually here. And if we now start the game we can see that this will enter into a stable state. I just start it. And we have a stable state of Zero Generation. So this field here is exactly the same as if I do the following thing. If I have a square of different cells
and the square of different cells it won't have a new generation because it will enter at a stable state because each cell has three living neighbours. And that state is exactly the same as the previous state. So we have just a square. There are a number of tasks below the video. Check them out. Try to solve them before continuing to the next video. And this will give you more understanding on what exactly is an infinite field and the different cases of the infinite field.