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Generate and Plot N Points Picking Random Points on Triangle

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My task is to write a function that takes as input a positive integer n. We are asked to consider the traingle whose corner points are (0,0), (2,0), and (1,2). Let p0 = (1,1). The function's purpose is to generate and plot n points p1,p2, ... pn where pk is the point determined by randomly picking one of the three corners of the triangle, and letting pk be the midpoint between the chosen corner point and pk-1 for 1 <= k <= n. I have a small program written, but I have no clue where to go from there. Please help me to get started on finding a program that works. I am aware that this program does not do what I want, it is just a starting point. Here is what I have so far:
function ex3(n)
%
%
rng('shuffle')
x = zeros(1,n);
y = x;
k = 1;
while k <=n
x(k) = 2*rand;
y(k) = 1*rand;
if y(k) > 1/2*x(k)
k = k + 1;
end
end
Border_x = [0,2,2,0];
Border_y = [0,0,1,0];
plot(Border_x,Border_y,'r',x,y,'b.','markersize',1)
axis tight
axis equal

  1 Comment

Sophie Culhane
Sophie Culhane on 22 Oct 2020
I would appreciate a starting point and I should be able to figure out a program from there. Thank you.

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Accepted Answer

Alan Stevens
Alan Stevens on 22 Oct 2020
More like the following;
rng('shuffle');
n = 1000; % Set number of points as desired
% Let (0,0) be vertex 1, (0,2) be vertex 2, (1,2) be vertex 3
X = [0 2 1];
Y = [0 0 2];
x = zeros(1,n);
y = x;
x(1) = 0.5; y(1) = 0.1; % starting point (change as desired)
for i = 2:n
p = randi(3,1); % Choose 1 2 or 3 at random
x(i) = (X(p) + x(i-1))/2;
y(i) = (Y(p) + y(i-1))/2;
end
Border_x = [0,2,1,0];
Border_y = [0,0,2,0];
plot(Border_x,Border_y,'r',x,y,'b.','markersize',1)
axis tight
axis equal
This generates a triangular Sierpinski gasket (better with a larger value of n). See what effect changing the starting point has.

  3 Comments

Sophie Culhane
Sophie Culhane on 22 Oct 2020
This program did not work for me. Is there an alternative to this program that would also work?
Sophie Culhane
Sophie Culhane on 22 Oct 2020
I’m sorry I noticed a typo in one of my lines. This program works, thank you for the help!

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