Nanodevices have terrible properties for building Boolean logic systems: high defect rates, high variability, high death rates, drift, and (for the most part) only two terminals. Economical assembly requires that they be dynamical. We argue that strategies aimed at mitigating these limitations, such as defect avoidance/reconfiguration, or applying coding theory to circuit design, present severe scalability and reliability challenges. We instead propose to mitigate device shortcomings and exploit their dynamical character by building self-organizing, self-healing networks that implement massively parallel computations. The key idea is to exploit memristive nanodevice behavior to cheaply implement adaptive, recurrent networks, useful for complex pattern recognition problems. Pulse-based communication allows the designer to make trade-offs between power consumption and processing speed. Self-organization sidesteps the scalability issues of characterization, compilation and configuration. Network dynamics supplies a graceful response to device death. We present simulation results of such a network—a self-organized spatial filter array—that demonstrate its performance as a function of defects and device variation.