Flower of Life

Author

Eric W. Weisstein
July 8, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/FlowerofLife.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/FlowerofLife.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

Arc[x_]:={x,x+Pi}
ArcSixth[x_]:={x,x+Pi/3}
CosSin[x_]:={Cos[x],Sin[x]}

FlowerOfLife:=Module[{t=ArcTan[Sqrt[3]/5],r=Sqrt[7],(*a1=2.1;a2=1.;*)a1=2Pi/3,a2=Pi/3},Graphics[{Circle[{0,0},1],(*center circle*)Table[Circle[CosSin[2 Pi i/6],1],{i,0,5}],(*1st ring of circles*)Table[Circle[Sqrt[3] CosSin[2 Pi (i+1/2)/6],1],{i,0,5}],(*2nd ring of circles*)Table[Circle[2 CosSin[2 Pi i/6],1],{i,0,5}],(*3rd ring of circles*)(*2/3 Arcs Arcs*)Table[Circle[3 CosSin[2 Pi i/6],1,{2Pi/3+2 Pi i/6,4Pi/3+2 Pi i/6}],{i,0,5}],(*Half Arcs*)Circle[r CosSin[t],1,Arc[2Pi/3]],Circle[r CosSin[-t],1,Arc[Pi/3]],Circle[r CosSin[Pi-t],1,Arc[-2Pi/3]],Circle[r CosSin[Pi+t],1,Arc[-Pi/3]],Circle[r CosSin[Pi/2-Pi/6-t],1,Arc[2Pi/3]],Circle[r CosSin[Pi/2+Pi/6+t],1,Arc[-2Pi/3]],Circle[r CosSin[3Pi/2-Pi/6-t],1,Arc[-Pi/3]],Circle[r CosSin[3Pi/2+Pi/6+t],1,Arc[Pi/3]],Circle[r CosSin[Pi/3+t],1,Arc[-Pi]],Circle[r CosSin[2Pi/3-t],1,Arc[-Pi]],Circle[r CosSin[-(Pi/3+t)],1,Arc[0]],Circle[r CosSin[-(2Pi/3-t)],1,Arc[0]],Table[Circle[{i,2Sqrt[3]},1,ArcSixth[-Pi/2-Pi/6]],{i,-1,1}],Table[Circle[{i,-2Sqrt[3]},1,ArcSixth[Pi/2-Pi/6]],{i,-1,1}],Table[Circle[{5/2+i/2,3Sqrt[3]/2-i Sqrt[3]/2},1,ArcSixth[Pi]],{i,0,2}],Table[Circle[{-(5/2+i/2),3Sqrt[3]/2-i Sqrt[3]/2},1,ArcSixth[3Pi/2+Pi/6]],{i,0,2}],Table[Circle[{-(5/2+i/2),-(3Sqrt[3]/2-i Sqrt[3]/2)},1,ArcSixth[0]],{i,0,2}],Table[Circle[{5/2+i/2,-(3Sqrt[3]/2-i Sqrt[3]/2)},1,ArcSixth[Pi/2+Pi/6]],{i,0,2}]}//N]]

Graphics

Show[FlowerOfLife,AspectRatio->Automatic]