Efficient code for draw a sierpinski triangle with matlab

Question

Following is my code:

function sierpinski(A, B, C, n)
    if n == 0
        patch([A(1), B(1), C(1)], [A(2), B(2), C(2)], [0.0 0.0 0.0]);
    else
       sierpinski(A, (A + B)/2, (A + C)/2, n-1);
       sierpinski(B, (B + A)/2, (B + C)/2, n-1);
       sierpinski(C, (C + A)/2, (C + B)/2, n-1);
end

% sierpinski([0 0], [1 0], [.5 .8], 8)

It's not very effectly. I want to first generating all data then patched, but I don't know how to correctly used. Also, can my code be written use for loops?

Solution

Your idea to write one function to generate the data and another to plot it is a good one - it's often a good idea to separate data generation from processing, and processing from output. I would do it something like this:

function out = sierpinski(a, b, c, n)

    if n == 0
        out.xvals = [a(1), b(1), c(1)];
        out.yvals = [a(2), b(2), c(2)];
    else
        out1 = sierpinski(a, (a+b)/2, (a+c)/2, n-1);
        out2 = sierpinski(b, (a+b)/2, (b+c)/2, n-1);
        out3 = sierpinski(c, (a+c)/2, (b+c)/2, n-1);
        out = [out1, out2, out3];
    end

end

This creates a struct of length 3^n, each entry of which contains the coordinates of one of the small triangles in the sierpinski triangle. Your code to plot it might then look like

>> out = sierpinski([0,0], [1,0], [0.5, sqrt(3)/2], 8);
>> figure(); hold on;
>> for i = 1:length(out)
       patch(out(i).xvals, out(i).yvals, 'k');
   end

That crashes on my machine (it seems that Matlab doesn't handle thousands of patches on the same plot very well) but a similar loop which plots one point at the corner of each small triangle.

>> x = [out.xvals];
>> y = [out.yvals];
>> plot(x, y, '.');

which produces this plot

Comments

[matrix89]

Thanks for your help.

[Adnan Ali]

Can i get some help ? i want to make the same triangle, but m not getting the code. even how to add it in file. can i get code in email or here. some thing like that ?

[Chris Taylor]

The code is already in my answer. If you explain what it is you don't understand then maybe I can help, but just saying "I'm not getting the code" won't get you very far.

[Elin]

Welcome to Stack Overflow! Answers should explain in words how they answer the question in addition to showing the code.

[Giuseppe Cardillo]

ok, sorry, It was my first comment. for each recursion level, you can 'erase' the central triangles, so you have to patch much more less triangles. For example, at first level, you have three 'up' triangles and only one 'down' triangle. You can path this, instead of the other three

[Giuseppe Cardillo]

a more compact routine is: function sierpinski(rec) [x, x0] = deal(cat(3, [1 0]', [-1 0]', [0 sqrt(3)]')); for k = 1 : rec x = x(:,:) + x0 * 2 ^ k / 2; end patch('Faces', reshape(1 : 3 * 3 ^ k, 3, '')', 'Vertices', x(:,:)') end

[Elin]

I tried to edit your comments in, please let me know if the code is wrong I may have not done the right line endings etc.