R=0.5;
θ0= 1/12;
r[θ_]:=R Sin[π(θ-θ0+If[θ<θ0,1,0])/2];
d[θ_]:=Disk[{Cos[2π θ],Sin[2 π θ]},r[θ]];
h[θ_]:=Hue[0.5+θ/20,θ/2,1-θ/2,1];

θSet={1/10,1/9,1/8,1/7,1/6,1/5,1/4,0.315,0.395,1/2,0.64,13/16,1};

logo = Graphics[Table[{h[θ],d[θ]},{θ,θSet}]]

Export["/Users/jmf/Desktop/logo3.png",logo]