Plotting a bird using mathematical equation issue.

Hello, I saw these set of equations that plot a bird using circles (See Image Below). I was able to code it down and the plot does not seem to be correct. However, there are a few issues with my code and it would be great if anybody could help.

My questions are:

1. The plot does not seem to be right when I run it (see image below). Can you please check if the code is correct to get the same plot as in the image above?
2. If I wanted to animate the plot, how would I do it?

clear; close all; clc;
A =@(k) sin((pi*k)./20000);
B =@(k) cos((31*pi*k)./10000);
C =@(k) sin((6*pi*k)./10000);
D =@(k) cos((31*pi*k)./10000);
E =@(k) sin((pi/2)*((k-10000)./(10000)).^7-(pi/5));
F =@(k) cos((pi/2)*((k-10000)./(10000)).^7-(pi/5));
G =@(k) sin((3*pi*k)./20000);
H =@(k) cos((3*pi)*((k-10000)./(100000)));
I =@(k) cos((9*pi)*((k-10000)./(100000)));
J =@(k) cos((36*pi)*((k-10000)./(100000)));
K =@(k) cos(((31*pi*k)./(10000))+((25*pi)/32));
L =@(k) cos((62*pi*k)./10000);

x = 1:9830;

% these are the Xk values 
Xk = A(x).^12 .* (0.5*B(x).^16.*C(x) + (1/6)*D(x).^20) + ((3*x)./20000) ...
    + B(x).^6 .*E(x);

% these are the Yk vlues
Yk = (-9/4)*B(x).^6.*F(x).*((2/3)+(A(x).*G(x)).^6) + ...
    (3/4)*H(x).^10.*I(x).^10.*J(x).^14 +...
    (7/10)*((x-10000)./(100000)).^2;

% This are the Rk values
Rk = A(x).^10.*((1/4)*K(x).^20 + (1/20)*B(x).^2) + (1/30).*((3/2)-L(x).^2);

figure()
scatter(Xk,Yk,[],Rk)
colormap(jet)

The plot looks like this:

Answer 1

[KSSV]

You need to modify the radius Rk so that, it gives the look.

clear; close all; clc;
A =@(k) sin((pi*k)./20000);
B =@(k) cos((31*pi*k)./10000);
C =@(k) sin((6*pi*k)./10000);
D =@(k) cos((31*pi*k)./10000);
E =@(k) sin((pi/2)*((k-10000)./(10000)).^7-(pi/5));
F =@(k) cos((pi/2)*((k-10000)./(10000)).^7-(pi/5));
G =@(k) sin((3*pi*k)./20000);
H =@(k) cos((3*pi)*((k-10000)./(100000)));
I =@(k) cos((9*pi)*((k-10000)./(100000)));
J =@(k) cos((36*pi)*((k-10000)./(100000)));
K =@(k) cos(((31*pi*k)./(10000))+((25*pi)/32));
L =@(k) cos((62*pi*k)./10000);

x = 1:9830;

% these are the Xk values 
Xk = A(x).^12 .* (0.5*B(x).^16.*C(x) + (1/6)*D(x).^20) + ((3*x)./20000) ...
    + B(x).^6 .*E(x);

% these are the Yk vlues
Yk = (-9/4)*B(x).^6.*F(x).*((2/3)+(A(x).*G(x)).^6) + ...
    (3/4)*H(x).^10.*I(x).^10.*J(x).^14 +...
    (7/10)*((x-10000)./(100000)).^2;

% This are the Rk values
Rk = A(x).^10.*((1/4)*K(x).^20 + (1/20)*B(x).^2) + (1/30).*((3/2)-L(x).^2);

figure()
scatter(Xk,Yk,Rk*8000,Rk)
colormap(jet)
axis equal

[Ahmed Mohamed Mansoor]

This is great!.

So it is just manipulating the radius of all the circles. Thank you so much.

In addition to that, if i wanted a quick animation of it. How would i do it?

[Benjamin Thompson]

So my answer that the scatter plot call needed changed was also correct?

[KSSV]

How you are expecting an animation?

[Ahmed Mohamed Mansoor]

@Benjamin Thompson

Matter of fact. Yes. You were correct. Sorry about not considering your comment. and thank you for pointing that out.

[Ahmed Mohamed Mansoor]

@KSSV

For example I tried to use comet but it did not seem to work.

Can I also ask another question. The beak of the bird at the very top seemes to be different from the actual piture. Any idea why this happens?

Answer 2

[Benjamin Thompson]

The radius values Rk do not seem to be used properly. Are you calling scatter correctly? Looks like maybe you need three arguments instead of 4.

[Ahmed Mohamed Mansoor]

oh. I am still a little new to this. But from what I know the use of scatter is okay. The scatter function maps the elements in Rk to colors in the current colormap as far as I know.

But any help would do.