Ellipse around Circle problem

Any idea how I could make the ellipses go around the circle to make a flower?

Here's the code:

clf
figure;
t=0:0.01:2*pi;
x=10*cos(t);
y=3*sin(t);
for i=1:12
    hold on;
    q=[x;y];
    e=pi/12*i;
    z=[cos(e) -sin(e);sin(e) cos(e)];
    k=z*q;
    r=k(1,:);
    d=k(2,:);
    plot(r,d);
    axis square;
    pause(1);
end
hold on;
drawCircle(0,0,1); 

[Walter Roberson]

How does this differ from your earlier questions ?

Answer 1

[Yusuf Suer Erdem]

That is the required code below. The red one with the dashed line is the circle and the other ones are the ellipses around it. You could increase the quantity of ellipses by using other type of formulas or you could try to rotate the existing ones.

clc; clear; close all;

C = [0 0] ;  % center 
a = 2.5 ;      % major axis 
e = 0.8 ;    % eccentricity 
b = a*sqrt(1-e^2) ; % minor axis 

R = 2;  % Radius if cricle 
th = linspace(0,2*pi) ; 

% Ellipse 
xe = C(1)+a*cos(th) ; 
ye = C(2)+b*sin(th) ; 
% Ellipse
xe2 = C(1)+b*cos(th) ; 
ye2 = C(2)+a*sin(th) ; 

% Circle 
xc = C(1)+R*cos(th) ;
yc = C(2)+R*sin(th) ;

% plot
plot(xe,ye,'b',xe2,ye2,'g',xc,yc,'r--')
axis equal

[Gashi]

Unfortunately this still leaves me with the same problem, here's a picture of what it is supposed to look like!

[Gashi]

[Yusuf Suer Erdem]

I changed the codes into that way. And the graph is below. For the missing ellipses, you need to identify the center points and add these ellipses to these points. After you need to rotate them according to the required angle without changing their sizes.

clc; clear; close all;

CC = [0 0] ; 
CE = [0 1.5] ;
CE2= [1.5 0] ;
CE3= [0 -1.5];
CE4= [-1.5 0];

a = 0.5 ;      
e = 0.8 ;    
b = a*sqrt(1-e^2) ; 
R = 0.5;  
th = linspace(0,2*pi) ; 

xe = CE(1)+b*cos(th) ; 
ye = CE(2)+a*sin(th) ; 

xe2 = CE2(1)+a*cos(th) ; 
ye2 = CE2(2)+b*sin(th) ; 

xe3 = CE3(1)+b*cos(th) ; 
ye3 = CE3(2)+a*sin(th) ; 

xe4 = CE4(1)+a*cos(th) ; 
ye4 = CE4(2)+b*sin(th) ; 

xc = CC(1)+R*cos(th) ;
yc = CC(2)+R*sin(th) ;

plot(xe,ye,'b',xe2,ye2,'g',xe3,ye3,'y',xe4,ye4,'c',xc,yc,'r--')
axis equal

[Gashi]

Nice! Thank you so much! :)