The developing brain undergoes a remarkable process of synaptic changes. To investigate the developmental changes in glutamatergic synaptic connections using the whole-cell patch clamp method, evoked excitatory postsynaptic currents (eEPSCs) were recorded from locus coeruleus (LC) neurons, a brain region crucial for cognitive functions, in rats at ages 7, 14, and 21 days. We employed fractal analysis to compute fractal dimensions of AMPA and NMDA receptors, serving as markers for synaptic maturation. Our findings revealed a significant increase in fractal dimensions during the third postnatal week and hence a developmental chenge of synaptic connections. A strong positive correlation between amplitude and fractal dimensions, in Pearson correlation analysis suggested that the synaptic currents' amplitude is closely related to the fractal properties of the receptors. A linear relationship between fractal dimensions and age indicated that fractal analysis can be a robust tool for predicting developmental changes. Additionally, we employed machine learning techniques to predict developmental changes based on AMPA and NMDA receptors. Support Vector Machine (SVM) models outperformed random forest models in accurately predicting age-dependent developmental changes, as indicated by the area under the curve (AUC) values. SVM achieved an AUC of 0.89 for AMPA receptors and 0.86 for NMDA receptors, demonstrating the effectiveness of fractal-based features in characterizing synaptic maturation. This study offers valuable insights into synaptic development in the LC nucleus and demonstrates the potential of fractal analysis as a tool to understand brain plasticity and early development. Fractal dimensions play a crucial role in characterizing the maturation of glutamatergic synapses and neural circuitry development.