How do I define the are of checkboard

Hello, I have a problem for with area of integration in Monte Carlo method.

The script for the integrated 2D function I used and worked is

    % square
    res = (abs(x)<= a ) && (abs(y)<= a );
    % circle
    res = ( (x^2 + y^2) <= a^2 );

where res being the map or area where I want to integrate, a = 1 for these purposes and x and y are the variables of f(x,y).

Now the map I want looks like the one on the picture. I've tried cycles and writing all the conditions for x and y but nothing works. Can you please help ?

Answer 1

[Parag]

It looks like you are trying to define an integration area in MATLAB using a Monte Carlo method. The image shows a checkerboard-like pattern within a square region. To define such a region in MATLAB, you need to apply a condition that alternates between included and excluded areas.

Here’s how you can define the checkerboard pattern in MATLAB:

% Define grid resolution 
n = 100; 
x = linspace(-1,1,n); 
y = linspace(-1,1,n); 
[X, Y] = meshgrid(x, y); 

% Define checkerboard pattern (3x3 grid) 
a = 2/3; % Size of each square in the 3x3 grid 
res = mod(floor((X + 1) / a) + floor((Y + 1) / a), 2) == 1; 

% Plot the region 
figure; 
imagesc(x, y, res); 
colormap(gray); 
axis equal;