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
I hope this provides the relevant information.
