Wolfram Language (Mathematica), 7170 bytes
Graphics@Line@Partition[NestWhileList[If[2∣#,#Graphics@Line@Last@Reap[#/2,3#+1]&,#/.a_/;a>1:>Last@Sow@{a,#>1&]If[2∣a,a/2,1]&3a+1]}]&
-1617 bytes from @att
63728127
Wolfram Language (Mathematica), 71 bytes
Graphics@Line@Partition[NestWhileList[If[2∣#,#/2,3#+1]&,#,#>1&],2,1]&
-16 bytes from @att
63728127
Wolfram Language (Mathematica), 70 bytes
Graphics@Line@Last@Reap[#//.a_/;a>1:>Last@Sow@{a,If[2∣a,a/2,3a+1]}]&
-17 bytes from @att
63728127
Wolfram Language (Mathematica), 7271 bytes
Graphics@Line@Partition[NestWhileList[If[OddQ@#,3#+1Graphics@Line@Partition[NestWhileList[If[2∣#,#/2]&2,3#+1]&,#,#>1&],2,1]&
-1516 bytes from @att
63728127
Wolfram Language (Mathematica), 72 bytes
Graphics@Line@Partition[NestWhileList[If[OddQ@#,3#+1,#/2]&,#,#>1&],2,1]&
-15 bytes from @att
63728127
Wolfram Language (Mathematica), 71 bytes
Graphics@Line@Partition[NestWhileList[If[2∣#,#/2,3#+1]&,#,#>1&],2,1]&
-16 bytes from @att
63728127
Wolfram Language (Mathematica), 8772 bytes
ListLinePlot[Partition[NestWhileList[If[OddQ@#Graphics@Line@Partition[NestWhileList[If[OddQ@#,3#+1,#/2]&,#,#>1&],2,1],PlotRange->All]&1]&
-15 bytes from @att
63728127
Wolfram Language (Mathematica), 87 bytes
ListLinePlot[Partition[NestWhileList[If[OddQ@#,3#+1,#/2]&,#,#>1&],2,1],PlotRange->All]&
63728127
Wolfram Language (Mathematica), 72 bytes
Graphics@Line@Partition[NestWhileList[If[OddQ@#,3#+1,#/2]&,#,#>1&],2,1]&
-15 bytes from @att
63728127