Here's the MatLab code to create a spirograph, I used it in conjunction with a 3D program to create a 3D spirograph, but this is it's core.


%%%%%%%% Spirograph Code %%%%%%%%%%

clear; clc; %Clean workspace.


%%%%% Imput Parameters (play with theese)
teethBig = 50; %Only integers please.
teethSmall = 26; %Only integers please.
penPosition = 1; %Any value (realistic drawing ocurr with values between 0 and 1)
%%%%%%%%%


%Calculate the number of revolutions to finish the drawing.
r0 = teethBig;
r1 = teethSmall;
while( r1 ~= 0 )
r2 = mod(r0,r1);
r0 = r1;
r1 = r2;
end
revolutions = teethSmall / r0;

%Create the driven variable.
theta = linspace(0,2*pi*revolutions,1000);

%Here is the meat of the process.
drawingX = (teethBig - teethSmall)*cos(theta) +...
penPosition*teethSmall*cos(-teethBig*theta/teethSmall);
drawingY = (teethBig - teethSmall)*sin(theta) +...
penPosition*teethSmall*sin(-teethBig*theta/teethSmall);


%Drawing the result.
plot(drawingX,drawingY,'lineWidth',2);
axis equal;
set(gca,'XTick',[]);
set(gca,'YTick',[]);

%%%%%%%% End Code %%%%%%%%%