A generalised model of biological topographic map development is presented which combines both weight plasticity and the formation and elimination of synapses (synaptic rewiring) as well as both activity-dependent and -independent processes. The question of whether an activity-dependent process can refine a mapping created by an activity-independent process is investigated using a statistical approach to analysingmapping quality. The model is then implemented in custom mixed-signal VLSI. Novel aspects of this implementation include: (1) a distributed and locally reprogrammable address-event receiver, with which large axonal fan-out does not reduce channel capacity; (2) an analogue current-mode circuit for Euclidean distance calculation which is suitable for operation across multiple chips; (3) slow probabilistic synaptic rewiring driven by (pseudo-)random noise; (4) the application of a very-low-current design technique to improving the stability of weights stored on capacitors; (5) exploiting transistor non-ideality to implement partially weightdependent spike-timing-dependent plasticity; (6) the use of the non-linear capacitance of MOSCAP devices to compensate for other non-linearities. The performance of the chip is characterised and it is shown that the fabricated chips are capable of implementing the model, resulting in biologically relevant behaviours such as activity-dependent reduction of the spatial variance of receptive fields. Complementing a fast synaptic weight change mechanism with a slow synapse rewiring mechanism is suggested as a method of increasing the stability of learned patterns.