Can anyone offer a simplified method of creating Conway's Game of life using nested for loops?

Need help evaluating array to follow the rules of Conway's game of life. Living cell 4 or more neighbors.... I also need the program to move one generation at a time.

[Guillaume]

What difficulty are you facing? It's not particularly difficult to code. You just have to count the number of neighbours of a cell and turn it on or off depending on that count.

The number of neighbours can be calculated any way you want, either by scanning all of them for each cell (a bit wasteful) or using 2d convolution (with a [1 1 1; 1 0 1; 1 1 1] kernel).

Answer 1

[Guillaume]

It's actually dead easy to implement in matlab, and you don't need for loops.

m = randi(2, 500) - 1;
while true      %use control C to stop
   imshow(m);
   drawnow;
   neighbours = conv2(m, [1 1 1; 1 0 1; 1 1 1], 'same');
   m = double((m & neighbours == 2) | neighbours == 3);
end

[Anthony]

This is true for a random function. What about for an array input by a user such as

name = input('Please enter the name of the file? ', 's'); file_name=[num2str(name) '.dat']; array=load(file_name);

end

array being any size

what would the parameters have to be set to evaluate the array for one generation of the game? Also using 0 for dead 1 for living.

It is a personal challenge to use nested for loops with a case statement to evaluate the entire array for the next generation.

[Guillaume]

I don't understand your comment about parameters

The first line of my code is just a way to generate a starting configuration for you to see how it works. You can replace it by anything you want, including a matrix loaded from a file.

The rest of the code does not care what the data is nor where it comes from. Each iteration of the loop is a generation of the game. You can of course replace the while loop by any sort of loop you want or remove it entirely. Again, it's just here to demo the code which is just the two lines:

neighbours = conv2(m, [1 1 1; 1 0 1; 1 1 1], 'same');  %calculate the number of neighbours
m = double((m & neighbours == 2) | neighbours == 3); %create a new generation

[Anthony]

sorry parameters...meant iteration of loops

[Guillaume]

I'm still not clear on what you're asking, the following would calculate the next generation of your array:

number = input('Please enter the number of the file? ', 's'); 
file_name= sprintf('%d.dat', number); 
array=load(file_name);
neighbours = conv2(array, [1 1 1; 1 0 1; 1 1 1], 'same');
array = double((array & neighbours == 2) | neighbours == 3);

If you want to put a for loop in there, you can always implement the convolution yourself or do an element by element computation of the matrix | and &.

[Anthony]

%User enters the name of file to load

name = input('Please enter the number of the file? ', 's');

%file extension is added

file_name=[num2str(name) '.dat'];

%the file which contains the array is assigned the name array

array=load(file_name);

%Convolution of the arrays neighbors

neighbours = conv2(array, [1 1 1; 1 0 1; 1 1 1]);

%array is returned with neighbors value

array = double((array & neighbours == 2) | neighbours == 3);

---------------------------------------------------------------------------

Gives me an error with the matrix dimensions

Error using & Matrix dimensions must agree.

Error in Untitled (line 5) array = double((array & neighbours == 2) | neighbours == 3);

I think the problem is I do not understand convolution. How can a for loop be manipulated to be equivalent to the argument in this code?

[Guillaume]

Oops, sorry I forgot the 'same' argument to conv2 to ensure that the neighbour matrix has the same size as the original matrix. I've edited all the posts to correct that now. The convolution should have been

neighbours = conv2(array, [1 1 1; 1 0 1; 1 1 1, 'same');

Ignoring edge issues, a convolution (with 'same', and odd-sized kernel) is equivalent to:

function m2 = conv2(m, kernel)
   m2 = zeros(size(m));
   kernel = fliplr(flipud(kernel)); %if you don't flip, it's a correlation
   halfheight = (size(kernel, 1)-1) / 2; %assuming odd size for kernel
   halfwidth =  (size(kernel, 2)-1) / 2; %assuming odd size for kernel
   for rowm = 1:size(m, 1)
      for colm = 1:size(m, 2)
         sum = 0;
         for rowk = 1:size(kernel, 1)
           for colk = 1:size(kernel, 2)
              sum = sum + m(rowm + rowk - halfheight, colm + colc - halfwidth);
           end
         end
         m2(rowm, colm) = sum;
      end
   end
end

Of course you would need to take care of the edges (usually you zero pad the original matrix by half the kernel size), but why bother implementing a slow way of doing it when there's already a fast way implemented in matlab.

[Anthony]

This is awesome. I have attached the array I am trying to manipulate. The only thing left appears to be an if statement that loops through the neighbor array and follows the rules of the game. Ex. more than 3 neighbors = dead. Am I going in the right direction?

[Guillaume]

I can't see any attachment.

The whole rules are encompassed in the one line:

array = double((array & neighbours == 2) | neighbours == 3)

A cell is live iff

• it is already live and has two neighbours
• or it has three neighbours

It covers both the keep alive rule (two or three neighbours), and the birth rule (3 neighbours).

You can replace that with for loops and if statements, but once again why?

for rowm = 1:size(m, 1)
   for colm = 1:size(m, 2)
      if (m(rowm, colm) == 1 && neighbours(rowm, colm) == 2) || neighbours(rowm, colm) == 3
         m(rowm, colm) = 1;
      else
         m(rowm, colm) = 0;
      end
   end
end

[Anthony]

Sorry. The file is attached. It is called array. I agree with you. I know it is complicated but I am supposed to be learning about nesting for loops with case statements. You don't even want to see the rest of the requirements for this program. I have to count the sum of living cells of each generation, create a plot using intrinsic function surf(x), label and color code plot, find the average of number of cells, etc.... The list goes on. Thank you for your help. I will probably post another question after I attempt to complete this grocery list of requirements for this program.