i want to sample all the possibilities (0, 45, 90deg) ranging from 5 to 25 layers. however, there are some contraints. for example, there should be no more than 3 45 deg. layers in a row in matlab

One way to solve this problem is by using nested loops and conditional statements. The outer loop will iterate over the number of layers from 5 to 25, and the inner loop will generate all possible combinations of angles (0, 45, 90 degrees) for that particular number of layers.

Within the inner loop, we can use a counter variable to keep track of the number of consecutive 45 degree layers. If we encounter a 45 degree layer, we increment the counter by 1. If the counter exceeds 3, we break out of the loop and move on to the next combination of angles.

Here's some sample code to show how this can be implemented:

main.m
min_layers = 5;
max_layers = 25;

for num_layers = min_layers:max_layers
    for i = 1:3^num_layers
        angles = dec2base(i-1, 3, num_layers) - '0' * 45;  % convert base 10 to base 3 and subtract 45
        is_valid = true;
        counter = 0;
        
        for j = 1:num_layers
            if angles(j) == 45
                counter = counter + 1;
                if counter > 3
                    is_valid = false;
                    break;
                end
            else
                counter = 0;
            end
        end
        
        if is_valid
            % do something with the valid combination of angles
        end
    end
end
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In this code, we use the dec2base function to convert the iteration index (which goes from 0 to 3^num_layers-1) from base 10 to base 3. We then subtract 45 from each digit to get the corresponding angle (0, 45, or 90 degrees).

We then iterate over the angles and use a counter to keep track of the number of consecutive 45 degree angles. If we encounter more than 3 consecutive 45 degree angles, we set the is_valid flag to false and break out of the loop.

Finally, if the combination of angles is valid, we can do something with it (e.g. store it in a matrix, plot a design, etc.).

Note that this method generates all possible combinations of angles, which can be computationally expensive for large numbers of layers. If you need to optimize this code for performance, there are more efficient ways to generate valid combinations (e.g. using a recursive function that generates only valid combinations).

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