Idriss J. Aberkane ∗ August 15, 2017 Abstract We investigate recurrent behaviors of the 1 (3x + 1) action (“Syr”) over the binary tree. The original composition of otherwise simple algebraic behaviors (eg: if a = 4b + 1, then Syr(a) = 4(Syr(b))) allows us to identify the existence of a relation merging orbits over alternate […]