How to write margolus code - Automata cellular

Dear community,

I would like to know if anyone has written a code for cellular automata with the neighborhood of Margolus.

Thanks.

JC.

Answer 1

[Abhijeet]

Hi Juan,

I understand that you want to implement the cellular automata with the neighborhood of Margolus.

Please refer to the following code snippet for the implementaion :-

function margolus_automaton
    % Size of the cellular automaton
    N = 50; % width and height of the grid
    T = 100; % number of time steps to simulate

    % Initialize the cellular automaton grid with random values
    grid = randi([0, 1], N, N);

    % Display initial state
    figure;
    imagesc(grid);
    colormap(gray);
    title('t = 0');
    pause(1);

    % Simulation loop
    for t = 1:T
        % Apply the Margolus neighborhood rules
        grid = applyMargolusRules(grid, mod(t,2) == 0);
        
        % Display current state
        imagesc(grid);
        colormap(gray);
        title(['t = ', num2str(t)]);
        pause(0.1); % Pause to visualize the update
    end
end

function newGrid = applyMargolusRules(grid, evenStep)
    [rows, cols] = size(grid);
    newGrid = grid; % Initialize new grid with the current state
    
    % Determine the offset for the block partitioning
    if evenStep
        rowOffset = 0;
        colOffset = 0;
    else
        rowOffset = 1;
        colOffset = 1;
    end
    
    % Iterate over 2x2 blocks with the given offset
    for i = 1:2:(rows-1)
        for j = 1:2:(cols-1)
            % Extract 2x2 block
            block = grid(mod(i-1+rowOffset:2+i-1+rowOffset, rows)+1, ...
                         mod(j-1+colOffset:2+j-1+colOffset, cols)+1);
            
            % Apply the rule to the block
            block = rot90(block); % Simple rotation rule
            
            % Write the updated block back to the new grid
            newGrid(mod(i-1+rowOffset:2+i-1+rowOffset, rows)+1, ...
                    mod(j-1+colOffset:2+j-1+colOffset, cols)+1) = block;
        end
    end
end

In the mentioned code above :-

• the function 'margolus_automaton' initializes a grid for the cellular automaton with random binary states and sets up the simulation parameters.After which it runs the simulation loop, applying Margolus neighborhood rules at each time step and updating the display.
• the function 'applyMargolusRules' determines the offset for block partitioning based on the current time step and applies the transition rules to each 2x2 block in the grid and then it returns the updated grid after applying the Margolus neighborhood transition rules for the current time step.

To know more about 'Margolus Neighbourhood' , please refer to the following reference link

• https://en.wikipedia.org/wiki/Block_cellular_automaton

I hope this provides the relevant information.