create the game of life in matlab

To create the Game of Life in MATLAB, we can follow the following steps:

1. Initialize the grid:

We can initialize the grid as an M x N matrix, with some cells alive and others as dead.

2. Define the rules:

• For a cell that is alive, if it has fewer than two live neighbors, it dies.
• For a cell that is alive, if it has two or three live neighbors, it survives.
• For a cell that is alive, if it has more than three live neighbors, it dies.
• For a cell that is dead, if it has exactly three live neighbors, it becomes alive.

3. Calculate the neighborhood:

For each cell in the grid, we need to calculate its neighborhood, defined as the 8 surrounding cells.

4. Iterate and update:

Create a loop that iterates over each cell in the grid, checks the number of live neighbors, applies the rule set, and updates the cell's state.

5. Visualize:

Use MATLAB's built-in functions to display the state of the grid at each iteration.

Here's an implementation in MATLAB:

main.m
% Parameters
M = 50; % Number of rows
N = 50; % Number of columns
generations = 1000; % Number of iterations

% Initialize the grid
grid = randi([0,1], M, N);

% Define the rules
for gen = 1:generations
    % Calculate the number of live neighbors
    neighbor_count = conv2(grid, [1 1 1; 1 0 1; 1 1 1], 'same');
    
    % Apply the rules
    grid((grid == 1) & (neighbor_count < 2)) = 0; % Death by under-population
    grid((grid == 1) & (neighbor_count > 3)) = 0; % Death by over-crowding
    grid((grid == 1) & ((neighbor_count == 2) | (neighbor_count == 3))) = 1; % Survival
    grid((grid == 0) & (neighbor_count == 3)) = 1; % Birth
    
    % Visualize the grid
    imagesc(grid);
    colormap(gray);
    pause(0.1);
end
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