(3n+1)/2ⁱ Predecessor Tree as a General Tree

(3n+1)/2ⁱ Predecessor Tree as a Binary Tree

Formation of the Abstract Predecessor Tree

                divide node contents into 3 equal subsets:
           {0 mod 3}             {2 mod 3}               {1 mod 3}
            leaves                   | s process             |  b process
                                     V                       V
                          {integers equally in       {integers equally in
                             {0, 1, 2} mod 3}           {0, 1, 2} mod 3}

Figure 3: One Cycle of the Iterative Development of the Abstract Generation Tree

                                      e

                                /  {8n+5}  \

                              /              \   
                       s                           b 

                  /          \                /          \
                ss           sb            bs             bb      
              /     \       /    \        /   \         /     \
            sss     ssb   sbs    sbb    bss    bsb    bbs     bbb 
             /  \   /  \   /  \  /  \    / \   / \    / \     / \