Plotting patters using circles and a trignometric equation

So here is an image I saw:

Based on these equations we should be able to plot something like this picture.

When i coded this down I got the pattern but does not look exactly like the picture. Is there a way to tweak this?

clear; close all; clc;

k = 1:14000;
a = pi*k./14000;

Xk = cos(10*a).*(1-0.5*cos(16*a).^2);
Yk = sin(10*a).*(1-0.5*cos(16*a).^2);

Rk = 1/200 + 0.1*sin(52*a).^4;

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

Answer 1

[Les Beckham]

k = 1:14000;
a = pi*k./14000;

Xk = cos(10*a).*(1-0.5*cos(16*a).^2);
Yk = sin(10*a).*(1-0.5*cos(16*a).^2);

Rk = 1/200 + 0.1*(sin(52*a)).^4;

figure()
% you need to specify the third argument, the size of the markers in points
% the factor 5000 is experimentally determined
scatter(Xk, Yk, Rk*5000, Rk) 
colormap(jet)
axis equal

Further experimenting would be needed to figure out how to get the colors right (the 4th argument to scatter). Here the colors are mapped based on the radius.

[Bjorn Gustavsson]

To QD-zeroth order the colour seems to depend on distance between the centre of the circles and the origin. The impression I get is that much (at least some) artistic handcraft will be required?

[Ahmed Mohamed Mansoor]

1) Thank you very much for the answer.

2) in terms of the colors, I feel a "copper" colormap makes it look nicer.

3) about the colors being mapped based on radius. That does make sense but I also think there is a third dimensional aspect to it, that has to do with the color scheme based on the depth of the image.

4) I think after processing the image they must have tweaked the color scheme I guess? But will keep playing around to see what i can come up with.

note: Apologies for accepting the answer late. Was not around for a couple of days.

[Les Beckham]

You are quite welcome. Better late than never :)