This paper introduces and investigates Complementary Power Dynamics, a novel class of iterated digit-power mappings defined by the transformation fP(n) = ∑ di^(P − di), where n ∈ ℕ and P ∈ ℕ with P ≥ 9. Under this mapping, each decimal digit di of n contributes to the successor state via an exponent equal to its complement relative to P. Utilizing a dedicated iterative computational engine (the Sufi Cycle Finder [10]), we empirically verify that for all tested parameters P ∈ {9, 10, 11, 12, 13, 14, 15, 16, 33, 100} and all n in ranges up to 1,000,000, every trajectory converges to a finite periodic orbit. We identify two classes of stable endpoints: fixed points and Harmony Cycles (periodic orbits of length L > 1). We establish analytically that n = 1 is a universal fixed point for all P ≥ 9, and provide a boundedness argument supporting the Convergence Conjecture. The attractor landscape exhibits non-monotone structural oscillation with P, while attractor magnitudes grow super-exponentially. These findings suggest that Complementary Power Dynamics constitutes a rich new domain within the study of discrete dynamical systems on the integers. One of the Harmony Cycles. P=9 Step-by-step path 345 -> 3^6 + 4^5 + 5^4 = 2378 2378 -> 2^7 + 3^6 + 7^2 + 8^1 = 914 914 -> 9^0 + 1^8 + 4^5 = 1026 1026 -> 1^8 + 0^9 + 2^7 + 6^3 = 345