Small addition to the presented 2D code to visualize each tube:
In[]:=
With[{n=20(*numberoftiles*),h=1/8(*widthofannulus*)},Graphics[{Black,GeometricTransformation[{Annulus[{-1/2,1/2},{1/2-h,1/2+h},{-Pi/2,0}],Annulus[{1/2,-1/2},{1/2-h,1/2+h},{Pi/2,Pi}]},Map[{RotationMatrix[RandomInteger[]Pi/2],#}&,Flatten[CoordinateBoundsArray[{{0,n},{0,n}},1,Center],1]]]}]]//​​ColorNegate//​​OperatorApplied[MorphologicalComponents][CornerNeighborsFalse]//​​Colorize//​​ColorNegate
Out[]=