function mutated_offspring = mutate(offspring, mutation_rate)
    mutated_offspring = offspring;

    for i = 1:size(offspring, 1)
        for j = 1:size(offspring, 2)
            if rand < mutation_rate
                % flip the bits
                mutated_offspring(i, j) = ~mutated_offspring(i,j);
            end
        end
    end
end