create hilbert curve in matlab

main.m
function hilbert_curve(order)
    % Initialize the Hilbert curve with a straight line, order 1
    curve = [0 0; 1 0; 1 1; 0 1];
    
    % Generate the curve up to the specified order
    for i = 2:order
        curve = hilbert_iterate(curve);
    end
    
    % Plot the Hilbert curve
    plot(curve(:,1), curve(:,2));
    axis equal;
    title(['Hilbert Curve of Order ', num2str(order)]);
end

function new_curve = hilbert_iterate(curve)
    % Rotation matrix for 90 degrees
    rotate90 = [0 -1; 1 0];
    
    % Generate new empty curve
    new_curve = [];
    
    for i = 1:size(curve, 1)-1
        p1 = curve(i,:);
        p2 = curve(i+1,:);
        
        % Calculate 4 points within the square
        new_points = [];
        for j = 0:3
            new_points(j+1,:) = (p1 + p2 + 1)/2 + 0.5^2 * rotate90^j * (p1 - p2);
        end
        
        new_curve = [new_curve; new_points(1:end-1, :); p2];
    end
end

% Generate Hilbert curve of order 3
order = 3;
hilbert_curve(order);
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