Abstract

The rapid expansion of Internet of Things (IoT) networks in smart environments such as smart cities, agriculture, and industrial monitoring has introduced significant challenges in energy-efficient communication. Existing routing protocols suffer from major limitations, including inability to handle heterogeneous node distribution, poor adaptation to topology irregularities, traffic congestion in dense regions, and unbalanced energy consumption, ultimately reducing network lifetime and stability. To overcome these issues, this study proposes a Fractal-Based Adaptive Routing (FBAR) framework that integrates fractal geometry principles into IoT routing design. The objective is to model multiscale network heterogeneity using Local Fractal Dimension and utilize it for adaptive routing decisions. The proposed method is implemented using a Python-based simulation environment, enabling scalable evaluation of IoT network behavior. The FBAR framework combines fractal topology analysis with energy-aware. cluster-head selection and relay node optimization. Simulation results show that the proposed method achieves a fractal dimension of 1.47, indicating strong self-similar structure in the network. Traffic intensity is effectively controlled with a maximum value of 1.42 in dense regions, while energy variance among cluster heads is reduced to 0.019. Additionally, the proposed approach extends network lifetime to approximately 3871 rounds, significantly outperforming LEACH, HEED, and DEEC protocols. These improvements correspond to an estimated performance gain of more than 55–60% in lifetime efficiency. The results confirm that fractal-aware modeling provides a powerful mathematical framework for optimizing routing performance in heterogeneous IoT networks, making FBAR a scalable and energy-efficient solution for next-generation smart systems.