This document develops the dynamic component of the BBF framework by analyzing how dyadic height and odd‑index structure evolve under elementary integer transformations. Building on the static coordinate representation introduced in article A01( see lelated work), the manuscript studies the interaction between horizontal dyadic reduction and vertical odd‑index progression. The BBF_a and BBF_d representations are examined in their dynamic behavior, with particular focus on height´and depth contraction, and the structural constraints linking both axes. The work establishes the fundamental dynamical relations that complement the static matrix geometry developed in the predecessor article and form the basis for subsequent parts of the BBF series.