Pentagon fractal design
Sándor Kabai
Five pentagons are place around a pentagon, and then is repeated to create a fractal structure.
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fi=GoldenRatio;​​pv=Table[{Sin[i2Pi/5],Cos[i2Pi/5],0},{i,5}];​​pent=Polygon[pv];​​p1=Map[Translate[pent,#]&,fipv];​​(*Reducethesizetopent*)​​v1=Translate[Scale[{p1},1/fi^2{1,1,1},{0,0,0}],{0,0,0.001}];​​Graphics3D[{pent,Yellow,v1},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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p2=Map[Translate[v1,#]&,fipv];​​v2=Translate[Scale[{p2},1/fi^2{1,1,1},{0,0,0}],{0,0,0.002}];​​Graphics3D[{Cyan,v2},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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p3=Map[Translate[v2,#]&,fipv];​​v3=Translate[Scale[{p3},1/fi^2{1,1,1},{0,0,0}],{0,0,0.003}];​​Graphics3D[{Pink,v3},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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p4=Map[Translate[v3,#]&,fipv];​​v4=Translate[Scale[{p4},1/fi^2{1,1,1},{0,0,0}],{0,0,0.004}];​​Graphics3D[{Green,v4},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->400]
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p5=Map[Translate[v4,#]&,fipv];​​v5=Translate[Scale[{p5},1/fi^2{1,1,1},{0,0,0}],{0,0,0.006}];​​Graphics3D[{LightPurple,v5},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->500]
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​​Graphics3D[{Yellow,pent,Cyan,v1,Green,v2,Pink,v3,Yellow,v4,LightPurple,v5},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->500]
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