Memristor (memory resistor) is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device's terminals and the duration of this voltage's application. The memristor is a non-volatile memory because the specific resistance is retained until the application of another voltage. A memristor implements a material version of Boolean logic and thus any logical circuit can be constructed from memristors. We propose to fabricate in laboratory experiments an adaptive, self-organized disordered network of memristors. This practical fabrication will be backed up by rigorous computer simulation experiments. The memristor network is comprised of a conglomerate of conductive polymer fibres interspersed with particles of solid electrolyte. The conglomerate is placed on a matrix of micro-electrodes capable of recording voltage and generating current sources and sinks. Machine learning techniques will be applied in order to design logical schemes and basic arithmetical circuits.