You’re correct about the iterator in both directions, fixed versions below.
◼
  • Define the iterator for the Collatz conjecture:
    • In[]:=
    collatz[n_?EvenQ]:=n/2​​collatz[n_?OddQ]:=3n+1
    ◼
  • Compute the orbit of an integer:
    • In[]:=
    collatzList[n_]:=NestWhileList[collatz,n,Not@*EqualTo[1]]
    In[]:=
    collatzList[25]
    Out[]=
    {25,76,38,19,58,29,88,44,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1}
    ◼
  • Compute a graph of orbits:
    • In[]:=
    collatzTreeGraph[n_]:=EdgeDelete[ResourceFunction["NestWhileGraph"][collatz,Range[n],Not@*ConnectedGraphQ@*UndirectedGraph,VertexLabels->Automatic],14]//LayeredGraph
    In[]:=
    collatzTreeGraph[25]
    Out[]=
    ◼
  • For the reverse, first define the iterator that produces the branches:
    • In[]:=
    anticollatz[n_]:=With[{m=(n-1)/3},If[OddQ[m]&&m>1,{2n,m},{2n}]]
    ◼
  • Compute the tree down to a certain level:
    • In[]:=
    collatzTree[level_]:=NestTree[anticollatz,1,level]
    In[]:=
    collatzTree[12]
    Out[]=