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
采纳的回答
Alan Stevens
2020-10-22
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.
7 个评论
Sophie Culhane
2020-10-22
Alan Stevens
2020-10-22
Strange! What was the error message?
Sophie Culhane
2020-10-22
Thank you for the program, but it only covers part of the triangle's area (see attached). How could one make it cover the whole area?
Many thanks and kind regards,
Ana
openfig('untitled.fig');
But I cannot guarantee that the solution is correct.
Alan Stevens
2023-2-15
The object you've been asked to generate is known as a Sierpinski triangle. It is a fractal structure. The gaps are an intrinsic part of it!
Torsten
2023-2-15
The object you've been asked to generate is known as a Sierpinski triangle.
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