Recursion to generate fractal

Question

I used recursion to generate fractal and got the desired result but I think my code can be better

I started using MATLAB a few days ago and since than trying and learning new things.
Now this code generates the fractal exactly as I wanted but I feel like it can a little bit neater.
Any suggestions are welcome (even off topic but related to how to use MATLAB) as I am a beginner in MATLAB, they will definitely help me in future.

hold on
x=[0 1 1/2];                %Coordinates of a equilateral triangle 
fill(x,y,'k');
axis equal
axis off
abc(list)                   

function abc(listnew)
    if abs(listnew(1,1)-listnew(1,2))>0.002
        listold=listnew;
        t=size(listold,2)/3;
        for j=1:t
        listnew(1,(j-1)*3+1:j*3)=[(listold(1,(j-1)*3+2)+listold(1,(j-1)*3+1))/2  (listold(1,(j-1)*3+3)+listold(1,(j-1)*3+2))/2 (listold(1,(j-1)*3+1)+listold(1,(j-1)*3+3))/2];
        listnew(2,(j-1)*3+1:j*3)=[listold(2,(j-1)*3+1) (listold(2,(j-1)*3+3)+listold(2,(j-1)*3+2))/2 (listold(2,(j-1)*3+1)+listold(2,(j-1)*3+3))/2];
        end
        pause(2)
        tri(listnew);
        k=size(listnew,2)/3;
        for m=1:k
            f=(m-1)*(3^2);
            l(1,(f+1):(f+3))=[listold(1,(m-1)*3+1) listnew(1,(m-1)*3+1) listnew(1,(m-1)*3+3)];
            l(2,(f+1):(f+3))=[listold(2,(m-1)*3+1) listnew(2,(m-1)*3+1) listnew(2,(m-1)*3+3)];

            l(1,(f+4):(f+6))=[listnew(1,(m-1)*3+1) listold(1,(m-1)*3+2) listnew(1,(m-1)*3+2)];
            l(2,(f+4):(f+6))=[listnew(2,(m-1)*3+1) listold(2,(m-1)*3+2) listnew(2,(m-1)*3+2)];

            l(1,(f+7):(f+9))=[listnew(1,(m-1)*3+3) listnew(1,(m-1)*3+2) listold(1,(m-1)*3+3)];
            l(2,(f+7):(f+9))=[listnew(2,(m-1)*3+3) listnew(2,(m-1)*3+2) listold(2,(m-1)*3+3)];
        end
        abc(l);
    end
end

function tri(list)
    for i =1:(size(list,2)/3)
        fill(list(1,(i-1)*3+1:i*3),list(2,(i-1)*3+1:i*3),'w');
    end
end

Answer 1

Though MATLAB allows to expand the size of a matrix by assigning to elements outside its bounds, it is always best to preallocate the array to its final size.

The for m=1:k loop has a lot of repeated code. First, m is always used as m-1. You could instead do for m=0:k-1 and simplify the code a bit. Next,

l(1,(f+1):(f+3))=[listold(1,(m-1)*3+1) listnew(1,(m-1)*3+1) listnew(1,(m-1)*3+3)];

can be written as

l(1,(f+1):(f+3)) = listold(1,(m-1)*3+[1,1,3]);

and you do the same for both elements along the 1 dimension, which can be written as

l(:,(f+1):(f+3)) = listold(:,(m-1)*3+[1,1,3]);

All 6 statements in this loop can be summarized as

l(:,(f+1):(f+9)) = listold(:,(m-1)*3+[1,1,3,1,2,2,3,2,3]);

It is possible to replace the whole loop, but that just makes the code less readable, I don’t recommend it.

It is common in MATLAB code to not use spaces, but I think code is more readable with spaces in it. Especially around the = assignment operator. In any case, make sure you use consistent spacing, for i =1:(size(list,2)/3) is rather unsettling to me. ;)

Likewise, be consistent with indentation. The loop for j=1:t is not indented.