gistlib - cellular automata in matlab

To simulate cellular automata in MATLAB, follow these steps:

Define the initial state of your cellular automaton. This can be represented as a binary matrix, with ones representing live cells and zeros representing dead ones.


% Create a 10x10 random binary matrix as the initial state of the cellular automaton
initialState = randi([0 1], 10, 10);
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Define the rules that dictate the behavior of your cellular automaton. This is usually done using a rule table, where each row represents a unique combination of the states of the three cells (current cell and its two neighbors) and the corresponding new state.


% Define the rule table for the classic "Game of Life" cellular automaton
ruleTable = [0 0 0 0 0;
             0 0 0 1 0;
             0 0 1 1 0;
             0 0 1 0 0;
             0 1 0 0 0;
             0 1 0 1 1;
             0 1 1 1 1;
             0 1 1 0 1;
             1 0 0 0 0;
             1 0 0 1 0;
             1 0 1 1 0;
             1 0 1 0 0;
             1 1 0 0 0;
             1 1 0 1 1;
             1 1 1 1 1;
             1 1 1 0 1];
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Use a loop to simulate the evolution of your cellular automaton over time. In each iteration, apply the rules to each cell to determine its new state.


% Initialize the current state of the cellular automaton
currentState = initialState;

% Iterate over a specified number of time steps
numSteps = 100;
for i = 1:numSteps
    % Apply the rules to each cell to determine its new state
    nextState = zeros(size(currentState));
    [rows, cols] = size(currentState);
    for r = 1:rows
        for c = 1:cols
            % Extract the state of the current cell and its two neighbors
            neighbors = zeros(1, 3);
            if r > 1
                neighbors(1) = currentState(r-1, c);
            end
            neighbors(2) = currentState(r, c);
            if r < rows
                neighbors(3) = currentState(r+1, c);
            end
            
            % Look up the new state of the current cell based on the rule table
            idx = bi2de(neighbors, 'left-msb') + 1;
            nextState(r, c) = ruleTable(idx, 5);
        end
    end
    
    % Update the current state of the cellular automaton
    currentState = nextState;
    
    % Visualize the current state of the cellular automaton
    imagesc(currentState);
    colormap(gray);
    axis off;
    drawnow;
end
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Visualize the evolution of your cellular automaton over time. One way to do this is to use the imagesc function to display the binary matrix as an image, with live cells shown in white and dead cells shown in black. You can also use the colormap function to customize the color scheme, and the axis and drawnow functions to update the display.


% Visualize the final state of the cellular automaton
imagesc(currentState);
colormap(gray);
axis off;
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cellular automata in matlab

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