Points are placed on a spiral with constant angular spacing. If the angular spacing is 2 Pi / Golden ratio, then the number of right spirals and the number of left spirals depicted by the points are two adjacent Fibonacci numbers. In the demonstration shown below the subsequent points are connected with lines. The points can be substituted with any object.
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Dynamic[Manipulate[points={PointSize[0.02],Point[Table[{rSin[r],rCos[r],0},{r,0,grow,2Pi/turn}]]};spiral=Line[Table[{rSin[r],rCos[r],0},{r,0,grow,Pi/30}]];lines=Line[Table[{rSin[r],rCos[r],0},{r,0,grow,2Pi/turn}]];Graphics3D[{points,spiral,lines},BoxedFalse,ViewPoint{0,0,4}],{{turn,1.618,"turning angle"},0,Pi},{{grow,20,"grow"},10,120},TrackedSymbols->{turn,grow}]]
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Dynamic[Manipulate[fib={PointSize[0.012],Point[Table[{rSin[r],rCos[r],0},{r,in,out,2Pi/1.618}]]};Graphics3D[fib,BoxedFalse,ViewPoint{0,0,4}],{{in,100,"minimum"},0,1000,1},{{out,2000,"maximum"},0,2000,1},TrackedSymbols{in,out}]]
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sp=Sphere[{0,0,0},40];dod=Scale[PolyhedronData["Dodecahedron","Faces"],30];vert=Table[{rSin[r],rCos[r],0},{r,150,1000,2Pi/1.618}];ob=Map[Translate[dod,#]&,vert];Graphics3D[ob,BoxedFalse,ViewPoint{0,0,4}]
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