Sierpinski Triangle in MATLAB - matlab

Question

I have written the following code but I seem to be missing something and I'm not sure what it is:
axis off
hold on
for i = 1:10000
r = [rand() rand()];
rp = [(1 - sqrt(r(1))) * -1 + (sqrt(r(1)) * (1 - r(2))) * 0 + (sqrt(r(1)) * r(2)) * 1,
(1 - sqrt(r(1))) * 0 + (sqrt(r(1)) * (1 - r(2))) * sqrt(3) + (sqrt(r(1)) * r(2)) * 0];
v1 = [-1 0 1];
v2 = [0 sqrt(3) 0];
num = randi([1 3], 1);
rv = [v1(num) v2(num)];
mid_x = (rp(1) + rv(1))/2;
mid_y = (rp(2) + rv(2))/2;
plot(mid_x, mid_y, '.r', 'MarkerSize', 0.000001)
end
this is what I'm getting instead:
triangle
Does anyone know how to fix it?

Answer 1

I see two issues:
You've reset r to a random value each time through the loop and then performed a computation that puts it in one of the three sub-triangles that appear in your image. Rather than doing that, you should redefine r each time in terms of its previous value. That's the basic idea behind iteration in general.
I'm not sure what the computation involving the square root is for. The basic computation for a Sierpinski triangle simply moves the current point r half the way to one of the three vertices of the triangle, which is randomly chosen. That's correctly done in your definition of mid_x and mid_y.
Taking this all into account, we get something that looks like so:
axis off
hold on
r = [rand() rand()]; % Define initial value of r outside the loop
v1 = [-1 0 1];
v2 = [0 sqrt(3) 0];
for i = 1:10000
num = randi([1 3], 1);
rv = [v1(num) v2(num)];
mid_x = (r(1) + rv(1))/2;
mid_y = (r(2) + rv(2))/2;
r = [mid_x mid_y]; % Redefine r each time through the loop
plot(mid_x, mid_y, '.r', 'MarkerSize', 0.000001)
end