Runtime Error while implementing own classes

I am trying to display Conways Game of life on a 32x64 RGB LED Matrix screen using the arduino uno

I am implementing it, using a class that represents each cell(LED’) in the Matrix and than another class that controls all the cells(LED’s) in the matrix, which represents the matrix.

Initially I coded a working version that I tested on the g++ compiler, working with multiple sizes of matrices (NxM). I than tested smaller sizes of matrices(5x5) in the arduino IDE, and everything worked up to the point, which I want.

As soon as I increase the matrices size to some unknown value,(around 10x10) my Arduino stops to work during runtime and I have no compiling issue.

Sketch uses 6,220 bytes (19%) of program storage space. Maximum is 32,256 bytes.
Global variables use 406 bytes (19%) of dynamic memory, leaving 1,642 bytes for local variables. Maximum is 2,048 bytes. (for a size of 32x64 matrix)

I manually allocate memory for the matrix, and for each block memory, I link an instance of a cell type, in a for loop.

It is in this for-loop that my arduino stops during runtime, I know this, since its stops printing messages to the console during this for-loop

int i;
  int r;
 for(i = 0; i < ROW_S*COL_S ; i++){    ROW_S = row sizes, COL_S = column size
       r = rand()%2;
       Serial.print(j);
        Serial.println(" Cell created");
      *(startPoint+i) = cell(r);
      delay(15);
     }

And just for extra info(I am not sure if this helps)

   int cell_size = sizeof(cell);      
   int grid_size = sizeof(GRID);

Output from console:
grid_size = 24
cell_size = 4

cell is the class name that represents each LED
GRID is the class name that represents the matrix that controls all the LEDS

Any pointers or directions to a possible solutions would be appreciated
Thanks

EDIT:
It seems it could be the SRAM, should I move to the Arduino Mega? And is there a way to possibly know how much SRAM is going to be used?

And is there a way to possibly know how much SRAM is going to be used?

The amount of SRAM in use changes are the program runs. You are probably running out.

There are many things you can do, though.

Stop wasting SRAM. String literals do not need to be copied to SRAM at run time. Use the F() macro to stop that.
Serial.println(F(" Cell created"));

You aren't really using a grip that is large enough to need an int to hold it's length or width, are you?

For more ideas, post more snippets. For a complete solution, post ALL of your code.