Braindrop is the first mixed-signal neuromorphic system designed to be programmed at a high level of abstraction. Previous neuromorphic systems were programmed at the neurosynaptic level and required expert knowledge of the hardware to use. In stark contrast, Braindrop’s computations are specified as coupled nonlinear dynamical systems and synthesized to the hardware by an automated procedure. This procedure not only leverages Braindrop’s fabric of subthreshold analog circuits as dynamic computational primitives, it compensates for their mismatched and temperature-sensitive responses at the network level. Thus, a clean abstraction is presented to the user. Fabricated in a 28-nm FDSOI process, Braindrop integrates 4096 neurons in 0.65 sq-mm. Two innovations—sparse-encoding through analog spatial convolution and weighted spike-rate summation though digital accumulative thinning—cut digital traffic drastically, reducing the energy Braindrop consumes per equivalent synaptic operation to 380 fJ for typical network configurations.