  We investigate the hierarchical structure of processes using the mathematical
theory of operads. Information or material enters a given process as a stream
of inputs, and the process converts it to a stream of outputs. Output streams
can then be supplied to other processes in an organized manner, and the
resulting system of interconnected processes can itself be considered a macro
process. To model the inherent structure in this kind of system, we define an
operad $\mathcal{W}$ of black boxes and directed wiring diagrams, and we define
a $\mathcal{W}$-algebra $\mathcal{P}$ of processes (which we call propagators,
after Radul and Sussman). Previous operadic models of wiring diagrams use
undirected wires without length, useful for modeling static systems of
constraints, whereas we use directed wires with length, useful for modeling
dynamic flows of information. We give multiple examples throughout to ground
the ideas.
