WING VI · DYNAMO
Every circuit in this wing is the same handful of facts about charge, current and field, looked at five times. A resistor, an inductor and a capacitor disagree about when a voltage should turn into a current — that argument, refereed at every possible frequency, is the entire subject. Nothing you build here is a metaphor for the real thing; it is the real thing, run at a speed and a scale you can watch.
EXHIBIT I · RESONANCE
A resistor, an inductor and a capacitor pull against each other at every frequency except one — the frequency where the inductor's lag and the capacitor's lead cancel exactly, and the circuit looks purely resistive to whatever is driving it. Everywhere else the current disagrees with the voltage about timing, and how sharply that disagreement narrows around the one true frequency is a single number: Q.
Raise R and watch Q collapse — a lossier circuit rings less. The particles on the loop travel at a speed set by the instantaneous current at whatever frequency you're driving it, so at resonance they pulse fastest and most in step with the source; off it, they lag.
R, L, C reshape the peak · drive frequency slider moves the working point
EXHIBIT II · FOURIER SYNTHESIS
A square wave is not a different kind of wave from a sine — it is infinitely many of them, added, at frequencies f, 3f, 5f, 7f… and amplitudes falling as 1/n. Stop the sum anywhere and two things happen at once: it becomes audibly and visibly a square wave, and a stubborn overshoot appears right at the edge — and never shrinks, no matter how many more harmonics you add. That's Gibbs' phenomenon, and it is not a bug in the math.
Turn sound on and listen to the same coefficients driving a real oscillator, not a pre-recorded sample — you are hearing exactly the partial sum on screen, harmonic count included. Try AM and FM too: same wave, two different ways of hiding a message inside it.
harmonic count builds the wave · listen to hear it · try AM / FM
EXHIBIT III · DIGITAL LOGIC
Nothing in a NAND gate knows what a number is. Addition, in silicon, is what you get when enough gates that only know "both wires high" and "at least one wire high" are wired together in the right shape. A half adder is an XOR and an AND, side by side; a full adder is two half adders and one more OR, chained to carry a bit forward.
A counter is what you get when that shape is made to remember its own output — four flip-flops, each one toggled by the bit before it, ripple through every value from 0000 to 1111 with a visible, honest delay as the change propagates stage to stage. Nobody synchronised it for you; that delay is why synchronous counters got invented.
pick a circuit · step or run the clock · watch the truth table fill in
EXHIBIT IV · ELECTROMAGNETIC RADIATION
A dipole's field has two personalities depending on how many wavelengths away you're standing. Close in (kr ≪ 1) it looks like ordinary electrostatics, falling off as 1/r³. Far out (kr ≫ 1) that term has died away and what's left is the part that actually leaves — falling off only as 1/r, carrying energy to infinity forever. There's no wall between the two; only a crossover, drawn here as a dashed ring at kr=1.
Beside it, a transmission line shows the other half of the story: send a wave down a line into a mismatched load and some of it bounces back, interfering with itself into a standing wave whose nodes sit exactly a quarter-wavelength apart, no matter what the load is — only how deep the nulls go changes.
kr zoom on the field · pick a load on the line · watch VSWR
EXHIBIT V · FEEDBACK CONTROL
A cart-pole isn't a demo of a robot — it's the smallest possible example of a system that is unstable entirely on its own. Set the force to zero and the pole falls, full stop, exactly the way an unbalanced pencil does. It stays up only because a controller is constantly, correctly lying about how big a correction to make.
Tune Kp, Ki or Kd wrong and you can watch exactly which promise it broke — too little D and it oscillates itself apart; an unclamped I term keeps "remembering" a disturbance long after it's over, and visibly overcorrects for it. Kick it and watch the recovery.
P, I, D sliders · kick to disturb · toggle windup clamp on the integral