H fractal
Sándor Kabai
A T-shaped unit is assembled from three cylinders (representing the trunk and two branches of a tree). Two such units are placed on a larger cylinder to form another T-shaped unit. This procedure is repeated. You can tilt or twist the branches to see the H-fractal and various tree-like structures.
A T-shaped unit is assembled from three cylinders (representing the trunk and two branches of a tree). Two such units are placed on a larger cylinder to form another T-shaped unit. This procedure is repeated. You can tilt or twist the branches to see the H-fractal and various tree-like structures.
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Manipulate[aff=0.69;ext=1.1;trunk1=Cylinder[{{0,0,0},{0,0,10ext}},1];next=Cylinder[{{0,0,0},{0,0,10aff}},aff];left1=Translate[Rotate[Rotate[next,Pi/2+0.001-tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext}];right1=Translate[Rotate[Rotate[next,-Pi/2+0.001+tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext}];u1={left1,right1,trunk1};trunk2=Cylinder[{{0,0,0},{0,0,10ext/aff}},1/aff];left2=Translate[Rotate[Rotate[u1,Pi/2+0.001-tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff}];right2=Translate[Rotate[Rotate[u1,-Pi/2+0.001+tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff}];u2={trunk2,left2,right2};trunk3=Cylinder[{{0,0,0},{0,0,10ext/aff^2}},1/aff^2];left3=Translate[Rotate[Rotate[u2,Pi/2+0.001-tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^2}];right3=Translate[Rotate[Rotate[u2,-Pi/2+0.001+tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^2}];u3={trunk3,left3,right3};trunk4=Cylinder[{{0,0,0},{0,0,10ext/aff^3}},1/aff^3];left4=Translate[Rotate[Rotate[u3,Pi/2+0.001-tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^3}];right4=Translate[Rotate[Rotate[u3,-Pi/2+0.001+tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^3}];u4={trunk4,left4,right4};trunk5=Cylinder[{{0,0,0},{0,0,10ext/aff^4}},1/aff^4];left5=Translate[Rotate[Rotate[u4,Pi/2+0.001-tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^4}];right5=Translate[Rotate[Rotate[u4,-Pi/2+0.001+tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^4}];u5={trunk5,left5,right5};trunk6=Cylinder[{{0,0,0},{0,0,10ext/aff^5}},1/aff^5];left6=Translate[Rotate[Rotate[u5,Pi/2+0.001-tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^5}];right6=Translate[Rotate[Rotate[u5,-Pi/2+0.001+tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^5}];u6={trunk6,left6,right6};trunk7=Cylinder[{{0,0,0},{0,0,10ext/aff^6}},1/aff^6];left7=Translate[Rotate[Rotate[u6,Pi/2+0.001-tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^6}];right7=Translate[Rotate[Rotate[u6,-Pi/2+0.001+tilt,{1,0,0}],-twist,{0,0,1}],{0,0,10ext/aff^6}];Graphics3D[{EdgeForm[],trunk7,left7,right7},ImageSize{400,400},ViewPoint{10,0,-2},ViewAnglePi/35,BoxedFalse,SphericalRegionTrue],{{tilt,1,"tilt branch"},0,1.4,ImageSizeTiny},{{twist,0,"twist branch"},0,1.4,ImageSizeTiny},ControlPlacementLeft,TrackedSymbols{aff,ext,tilt,twist}]
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