Antoines Necklace

Antoines Necklace is a Cantor set style fractal in 3D that is credited to Louis Antoine, first documented in 1921. The recursive procedure is evident from the following images, each torus is replaced by N others. The angle between replacement torii is often 90 degrees but it need not be. The parameters of ring thickness, ring scale factor, number of rings and ring angle are constrained by the desire for the rings not to intersect.

thickness = 0.25, scale factor = 0.22, N = 20, tiltangle = 90

thickness = 0.2, scale factor = 0.32, N = 14, tiltangle = 60

thickness = 0.25, scale factor = 0.32, N = 15, tiltangle =70