Conventional electronics is founded on a paradigm where shaping perfect electrical elements is done at the fabrication plant, so as to make devices and systems identical, “eternally immutable.” In nature, morphogenic evolutions are observed in most living organisms and exploit topological plasticity as a low-resource mechanism for in operando manufacturing and computation. Often fractal, the resulting topologies feature an inherent disorder: a property that is never exploited in conventional electronics manufacturing, while necessary for data generation and security in software. In this study, we present how such properties can be exploited to implement long-term and evolvable synaptic plasticity in an electronic hardware. The rich topology of conducting polymer dendrites (CPDs) is exploited to program the non-ideality of their electrochemical capacitances containing constant-phase-elements. Their evolution through structural changes alters the characteristic time constants for them to charge and discharge with the applied voltage stimuli. Under a train of voltage spikes, the evolvable current relaxation of the electrochemical systems promotes short-term plasticity, with timescales ranging from milliseconds to seconds. This large window depends not only on the temporality of the voltage pulses used for reading but also on the structure of a pair of CPDs on two electrodes, grown by voltage pulses. This study demonstrates how relevant physically transient and non-ideal electrochemical components can be exploited for unconventional electronics, with the aim to mimic a universal property of living organisms, which could barely be replicated in a silicon monocrystal.