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The following code is meant to create a dynamic graphic of epicycles.
Clear["Global`*"]
T1=3;
T2=2;
a0=4;
a1=2;
k0=(2*Pi)/T2;
k1=(2*[Pi])/T1;
z0=a0*E^(I*k0*t);
z1=a1*E^(I*k1*t);
z2=z0+z1;
z3=z0+z1+z2;
z4=z0+z1+z2+z3;
z5=z0+z1+z2+z3+z4;
ptsList={{0,0},{Re[N[z0]],Im[N[z0]]},{Re[N[z1]],Im[N[z1]]},...