You missed the important part of the exercise in that the rings have to be interlocking :D

%% Init parameters
R = 0.9;
scale = 1.1;
N = 100;
thickness = 10;
angle = linspace(0,2*pi,N);

%% Plot the rings
y = R * sin(angle);
x = R * cos(angle);
plot(x,y,’b',x + scale * R,y - scale * R,’k',x + 2 * scale * R,y,’r',…
x + 3 * scale * R, y - scale * R,’g',x + 4 * scale * R,y,’k',…
‘LineWidth’,thickness);

%% Make axis look better
axis off;
set(gca,’XLim’,[-1.2 5.2]);
set(gcf,’Color’,[1 1 1]);

Thanks for an interesting and elegant solution!

–Loren

No need to add undulations, just alternate your axis (and I added an alternating offset) then increment the angles/offsets on each ring. (Of course they’re really ellipses in 3D but the 2D projection is circular. Actually, it looks kinda neat on Y-Z view.) (I wasn’t mathematically rigorous on what the coefficients should be for N rings, but I did try it out to 28 rings.)

N = 1000;
angle = linspace(pi/4,9*pi/4,N);

c=’bykgr’;
%c=’bykgrmcbykgrmcbykgrmcbykgrmc’;
index = 1:length(c);
UL=( ~mod(index,2) - mod(index,2) ); %negative if Upper ring, positive if Lower ring

h2 = figure(’color’,[1 1 1]);
hold on
for loop=1:length(c)
z = cos(angle + UL(loop)*pi/4) * … %alternating axes
(length(c)-loop)*0.1*-UL(loop) + … %alternating angles
.05*(length(c)-loop)*-UL(loop); %alternating depth offsets
x = cos(angle) * 0.9 + (loop-1);
y = sin(angle) * 0.9 - ~mod(loop,2);
plot3(x,y,z,[c(loop) ‘.’],’markersize’,10);
end
axis equal off
hold off

Thanks so much for sharing an entirely different approach!

–Loren

% first create a ‘ring’

x=sin(2*pi*(1/100)*(0:99));
y=cos(2*pi*(1/100)*(0:99));
c=zeros(32,32);
for i=1:100
c(ceil(15*x(i))+16,ceil(15*y(i))+16)=1;
end

% then create your canvas
A=zeros(128,128);

% set ring spacing
n=36;

% convolving this set of impulses with
% the ring will make the final output array
% the different values will change the colors
A(64,((0:2)*n)+20)=[1 3 5];
A(64+15,([1/2 3/2]*n)+20)=[2 4];

% use this to test the overlaps
D(64,((0:2)*n)+20)=[1 1 1];
D(64+15,([1/2 3/2]*n)+20)=[1 1];

w=conv2(D,c,’same’);

% find where the rings overlap
[s,t]=find(w==2);

f=[2 2 1 2 3 4 4 3 4 5];

% create the final output array
r=conv2(A,c,’same’);

% replace with the ‘right values from left to right
for ii=1:10
r(s(ii),t(ii))=f(ii);
end

% set the color map to a white background
% and five colors
map=[1 1 1 ; 0 0 1 ; 1 1 0 ; 0 0 0 ; 0 1 0 ; 1 0 0]

% display
imagesc(r)

colormap(map);