<p>This paper presents an adaptive control strategy for achieving anti-synchronization in transcendental alternated(odd and even functions) Julia sets. The system employs cosine-based transcendental mappings that works alternatively through iteration, generating complex Julia dynamics. Adaptive controllers are developed for both known and unknown set of parameters, with update laws incurred to estimate unknown coefficients of transcendental operators for the iterative schemes. Stability analysis of this article guarantees the convergence of the anti-synchronization error, while numerical results demonstrate rapid convergence and accurate parameter estimation of the control system. The article depicts the computational behavior of the system through the Average Number of Iterations (ANI) and time analysis, providing deeper insight into the convergence dynamics and efficiency of the iterative process. The proposed method enhances the stability and performance of transcendental alternated systems.</p>