Babbage's Difference Engine: Difference Table Plotter

Before electronic computers existed, Charles Babbage designed a machine that could tabulate polynomials using nothing but repeated addition, propagated through columns of decimal digit wheels connected by carry gearing. This 2D companion renders the same finite-difference arithmetic two ways at once: a rolling line plot traces f(n) point by point exactly as the engine's own stereotype printer would have stamped a table, while a cascade diagram beneath it shows the four difference registers as stacked value boxes with an animated addition pulse flowing upward — from the constant Δ³ register into Δ², into Δ¹, into f(n) — on every turn of the crank. Set the coefficients of a cubic polynomial, turn the crank by hand or let it run automatically, and watch the curve grow while the number of multiplications used stays at zero throughout: the entire reason the design was mechanically realisable with Victorian-era engineering.