I recommend playing Conway's Game of Life to observe the complexity of 2-dimensional systems. 'Golly' is a good open-source software for this purpose.
However, bear in mind the scale of your simulation:
If we take 1 dimension of 1 cell to be 1 Planck Length, the 2-D equivalence of a single atom would be about 1,000,000,000,000,000,000,000,000,000 x 1,000,000,000,000,000,000,000,000,000 cells. (don't attempt to actually run that, even if you have the patience to draw it! Your computer will crash)
If we take 1 generation to be 1 Planck Time, you would need to run that gigantic simulation of a '2-D atom' for about 100,000,000,000,000,000,000,000,000,000,000,000,000,000 generation to reach the equivalence of 1 second.