Closely mimicking the hierarchical structural topology with emerging behavioral functionalities of biological neural networks in neuromorphic devices is considered of prime importance for the realization of energy-efficient intelligent systems. In this article, we report an artificial synaptic network (ASN) comprising of hierarchical structures of isolated Al and Ag micro-nano structures developed via the utilization of a desiccated crack pattern, anisotropic dewetting, and self-formation. The strategically designed ASN, despite having multiple synaptic junctions between electrodes, exhibits a threshold switching (Vth ∼ 1-2 V) with an ultra-low energy requirement of ∼1.3 fJ per synaptic event. Several configurations of the order of hierarchy in the device architecture are studied comprehensively to identify the importance of the individual metallic components in contributing to the threshold switching and energy-minimization. The emerging potentiation behavior of the conductance (G) profile under electrical stimulation and its permanence beyond are realized over a wide current compliance range of 0.25 to 300 μA, broadly classifying the short- and long-term potentiation grounded on the characteristics of filamentary structures. The scale-free correlation of potentiation in the device hosting metallic filaments of diverse shapes and strengths could provide an ideal platform for understanding and replicating the complex behavior of the brain for neuromorphic computing.