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
