Can I get a MATLAB code on how to analyze Track irregularities data with Fractal dimension via a Ruler method?

I am trying to analyze track irregularities data with Fractal dimension on MATLAB using Ruler method, I am finding it difficult to develop the fractal dimension calculation algorithm.

Answer 1

[Nithin]

Hi Shakirudeen,

I understand that you want to analyze track irregularities data with Fractal dimension using Ruler method in MATLAB.

To Implement the same, kindly refer to the following example:

irregularities = [1.2, 2.3, 3.4, 4.5, 5.6, 6.7, 7.8, 8.9, 9.0, 10.1]; % example data
 
% Define a range of box sizes (ruler lengths)
box_sizes = 1:5:20;
 
% Initialize an array to store the number of boxes covering the data
num_boxes = zeros(size(box_sizes));
 
% Perform the ruler method
for i = 1:length(box_sizes)
    box_size = box_sizes(i);
    num_boxes(i) = count_boxes(irregularities, box_size);
end
 
% Fit a linear regression to the data to estimate the fractal dimension
coefficients = polyfit(log(box_sizes), log(num_boxes), 1);
fractal_dimension = -coefficients(1);

% Plot the results
figure;
plot(log(box_sizes), log(num_boxes), 'o-');
xlabel('log(Box Size)');
ylabel('log(Number of Boxes)');
title(['Fractal Dimension']);

% Function to count the number of boxes covering the data
function count = count_boxes(data, box_size)
    count = 0;
    for i = 1:length(data)
        x = data(i);
        % Check if the box of the given size covers the data point
        if abs(x) <= box_size / 2
            count = count + 1;
        end
    end
end

For more information regarding “polyfit”, kindly refer to the following documentation:

https://www.mathworks.com/help/matlab/ref/polyfit.html

I hope this answer helps you.

Regards,

Nithin Kumar.