Interconnectivity, fault tolerance, and dynamic evolution of the circuitry are long sought-after objectives of bio-inspired engineering. Here, we propose dendritic transistors composed of organic semiconductors as building blocks for neuromorphic computing. These devices, owning to their voltage-triggered growth and resemblance to neural structures, respond to action potentials to achieve complex brain-like features, such as Pavlovian learning, pattern recognition, and spike-timing-dependent plasticity. The dynamic formation of the connections is reminiscent of a biological learning mechanism known as synaptogenesis, and it is carried out by an electrochemical reaction that we name field-directed polymerization. We employ it to dendritic connections and, by modulating the growth parameters, control material properties such as the resistance and the time constants relevant for plasticity. We believe these results will inspire further research towards the complex integration of polymerized synapses for brain-inspired computing.