  We develop a theory of percolation with plasticity systems (PWPs) rendering
properties of interest for neuromorphic computing. Unlike the standard
percolation between two large electrodes, they have multiple ($N\gg 1$)
interfaces and exponentially large number ($N!$) of conductive pathways between
them. These pathways consist of non-ohmic random resistors that can undergo
bias induced nonvolatile modifications (plasticity). The neuromorphic
properties of PWPs include: multi-valued memory, high dimensionality and
nonlinearity capable of transforming input data into spatiotemporal patterns,
tunably fading memory ensuring outputs that depend more on recent inputs, and
no need for massive interconnects. A few conceptual examples of functionality
here are random number generation, matrix-vector multiplication, and
associative memory. Understanding PWP topology, statistics, and operations
opens a field of its own calling upon further theoretical and experimental
insights.
