Sine combinator.
A toy for building intuition about Fourier series — the claim that any periodic signal can be written as a sum of pure sines. Each row is one source, shown as a rotating phasor on the left and the wave it casts on the right; the bottom row is their sum, and the panel on the far right is that same composite plotted in the frequency domain. Use it to see how phase, frequency, and amplitude each shape a wave — to watch a square wave assemble from the first four odd harmonics (try square), or to spot the Gibbs ringing that always comes from truncating an infinite series.
What you're looking at.
Every sine wave is a rotation seen from the side. Mark a point on a circle, project its height onto a moving timeline, and you trace a sine. Each row above does this for one source: the circle's radius is the amplitude, how fast the dot rotates is the frequency, and the starting angle is the phase.
The bottom row sums all four sources. The little glyph on the left isn't a sigma — it's the four circles connected tip-to-tail. Each phasor pivots on the previous one's endpoint, and the final dot's height is the value of the composite wave at this instant. Stack the right harmonics and recognizable shapes appear: a square wave assembles itself from odd harmonics with amplitudes 4 / (πn); a sawtooth uses every harmonic with alternating signs; a triangle uses odd harmonics with a 1 / n² falloff. Fewer than infinite harmonics is why the corners ring — that's the Gibbs phenomenon.
The panel on the right is the same signal in the frequency domain — a stem for each source plotted at its frequency, with height equal to its amplitude. A pure sine is a single stem; a square wave is a neat ladder of stems at 1, 3, 5, 7 Hz. Time domain and frequency domain are the same information, looked at from two sides.