Difference, Not Differential

In Nonlinear Dynamics and Chaos, Steven H. Strogatz opens by naming two kinds of dynamical system: differential equations, which describe systems evolving in continuous time, and iterated maps — difference equations — which arise where time is discrete. Both are real; both are dynamics. Because differential equations are the more widely used in science and engineering, he makes a choice, and says so plainly: “Differential equations are used much more widely in science and engineering, and we shall therefore concentrate on them.”

— Steven H. Strogatz, Nonlinear Dynamics and Chaos, § 1.2, “The Importance of Being Nonlinear” (quoted verbatim; verified against the primary source)

Principia Attractum is where that road might have led had the other fork been taken. We concentrate on the one he set aside — the discrete one: not the next tick of a clock, but the next step of a structure’s own recursion, the next tik. Persistence, sovereignty, ignition, loss — everything here follows from that single change of foot.