Stocks and Flows

Recently I have gotten interested in stocks and flows. When combined with feedback and delays, they are revelatory. They are simple, yet their importance is only recently realized. In particular, J W Forrester founded system dynamics in the 60s. Because system dynamics is turning out to be the best hope for salvation from climate change, I feel a little guilty about applying it to my own silly projects. However, the temptation is too great, so I plan to use a dynamic system to make music. The beauty of it is, everything usually done with several different components, such as oscillators filters and sequencers, can be done with just stocks and flows in a topology. In a sense, stocks and flows are the fundamental constituents of musical instruments. Because computers are so fast, the timewheel algorithm is so efficient, and leverage of simple calculations is so great, I feel confident a corpuscular model of stocks and flows will suffice to provide sound of many different qualities. Consider a set of stocks of amounts. Rather than calculate how the amounts change as they flow from stock to stock, instead schedule fixed size corpuscles to be transferred. Large flows are modeled by frequent transfers, and small flows by infrequent transfers. Also scheduled are changes to the flow rates. To model feedback, simply make the changes to flow rates depend on stock amounts, and to model feedback delay, simply schedule the flow changes to take effect some time after their calculation. Because I am already in the middle of a project to model, display, and manipulate polytopes, I will use the polytope faces as flow gates between regions containing stock amounts at points in the regions. Thus polytopes form membranes that in general prevent flow, but have special faces that allow flow dependent on any/all stocks amounts at some prior time. Stocks, as points, reside in areas bounded by overlapping polytopes, and are fed and drained by special faces into their area.