Below is a full demo of how to do so in MATLAB, where m is the size of the vector and n is the number of rotations. The rotated vectors are saved in the matrix XY.
%% This is a demo to rotate your mx2 vector n times and generate a (mxn)x2
% matrix full of these resulting data points.
clear
clc
close all
%% Start with your values for m and n and calculate rotation matrix.
m = 6;
n = 50;
theta = 360/n;
R = [cosd(theta) -sind(theta);
sind(theta) cosd(theta)]';
%% Allocate space for the end matrix.
XY = zeros(m*n, 2);
%% Generate the first vector.
x = zeros(m, 1);
y = linspace(1, 1.5, m)';
xy = [x y];
XY(1:m, :) = xy;
%% Loop through and calculate rotated matrcies.
for i = 1+m:m:m*n
xy = xy*R;
XY(i:i+m-1, :) = xy;
end
%% Plot the results.
hold on
grid on
axis equal
ang = linspace(0,360,100);
xc = cosd(ang);
yc = sind(ang);
plot(xc, yc)
for k = 1:m:m*n
x = XY(k:k+m-1, 1);
y = XY(k:k+m-1, 2);
plot(x, y);
end
The result is the following:
