how to set up two different populations in a segregation model code?

I have a general code for the segregation model like the following:

%% n = grid_size;

grid_size = 50;

n = grid_size;

n2 = n^2;

grids = zeros(n);

emp = round((percent_empty/100)*n2);

two = round((percent_two/100)*n2);

tot = emp + two;

rand_loc = randperm(n2);

init_emp = rand_loc(1:emp);

init_two = rand_loc(emp+1:tot);

init_one = rand_loc(tot+1:end);

grids(init_emp) = 3;

grids(init_two) = 2;

grids(init_one) = 1;

figure, imagesc(grids), colorbar, axis([1 n 1 n]);

% frame = getframe;

% writeVideo(writerObj,frame);

how could I insert two populations in this code, that is population 1 are unsatis ed with their location if the number of their neighbours that are from population 2 is u1 or higher, and population 2 occupants are unsatis ed with their location if the number of their neighbours that are from population 1 is u2 or higher. Beside this, p1+p2 is less than 100; the rest can be empty.

Answer 1

[Abhinaya Kennedy]

Hi,

To modify the existing code to include two populations with specific satisfaction conditions, you would need to add functionality to:

• Define the satisfaction thresholds u1 and u2 for populations 1 and 2, respectively.
• Calculate the number of neighbours of each type surrounding each cell.
• Move unsatisfied occupants to empty cells until all occupants are satisfied or no more moves can be made.

Here's an outline of how you can modify the code to include these steps:

% Define the grid size and the percentages for each population
grid_size = 50;
percent_empty = 10; % You can set this value as needed
percent_one = 45;   % Population 1 percentage
percent_two = 45;   % Population 2 percentage

% Define satisfaction thresholds
u1 = 3; % Threshold for population 1
u2 = 3; % Threshold for population 2

% Initialize the grid
n = grid_size;
n2 = n^2;
grids = zeros(n);

% Calculate the number of each type
emp = round((percent_empty/100)*n2);
one = round((percent_one/100)*n2);
two = round((percent_two/100)*n2);

% Randomly assign initial locations
rand_loc = randperm(n2);
init_emp = rand_loc(1:emp);
init_one = rand_loc(emp+1:emp+one);
init_two = rand_loc(emp+one+1:end);

% Fill the grid with populations and empty spaces
grids(init_emp) = 0; % Empty cells
grids(init_one) = 1; % Population 1
grids(init_two) = 2; % Population 2

% Display the initial grid
figure, imagesc(grids), colorbar, axis square;

% Main loop to move unsatisfied occupants
max_iterations = 1000; % Set a maximum number of iterations to prevent infinite loop
iteration = 0;
while iteration < max_iterations
    iteration = iteration + 1;
    moved = false;
    
    for x = 1:n
        for y = 1:n
            if ~check_satisfaction(grids, x, y, u1, u2)
                % Find an empty cell to move to
                empty_cells = find(grids == 0);
                if ~isempty(empty_cells)
                    new_loc = empty_cells(randi(length(empty_cells)));
                    grids(new_loc) = grids(x, y); % Move occupant to the new location
                    grids(x, y) = 0; % Set old location to empty
                    moved = true;
                end
            end
        end
    end
    
    % Update the display
    figure, imagesc(grids), colorbar, axis square;
    
    % If no one moved in this iteration, everyone is satisfied
    if ~moved
        break;
    end
end

% Display the final grid
figure, imagesc(grids), colorbar, axis square;

% Function definitions must appear at the end of the file

% Function to calculate the number of neighbors of a given type
function count = count_neighbors(grids, x, y, neighbor_type)
    [rows, cols] = size(grids);
    count = 0;
    for i = -1:1
        for j = -1:1
            if ~(i == 0 && j == 0) && x+i > 0 && x+i <= rows && y+j > 0 && y+j <= cols
                if grids(x+i, y+j) == neighbor_type
                    count = count + 1;
                end
            end
        end
    end
end

% Function to determine if an occupant is satisfied
function is_satisfied = check_satisfaction(grids, x, y, u1, u2)
    if grids(x, y) == 1
        is_satisfied = count_neighbors(grids, x, y, 2) < u1;
    elseif grids(x, y) == 2
        is_satisfied = count_neighbors(grids, x, y, 1) < u2;
    else
        is_satisfied = true;
    end
end