How do I define the are of checkboard

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Leonard Valko
Leonard Valko 2020-5-28
回答： Parag 2025-1-31
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 ?

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回答（1 个）

Parag
Parag 2025-1-31
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;

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