There is a paper — Odrzywołek, All elementary functions from a single operator (arXiv:2603.21852) — that proves something quietly absurd: one binary operator,
eml(a, b) = e^a − ln b,
together with the constant 1, generates every elementary function. The
exponential, the logarithm, the identity, the whole trigonometric family —
all of it falls out of nesting that one operator over the constant one.
The background you are looking at is that machine. It grows random expression
trees from the grammar S → 1 | x | eml(S, S), evaluates them over the complex
plane, and sweeps each curve across a phosphor oscilloscope — the real part in
green, the imaginary part in blue. About one curve in three is a real
construction from the paper, surfacing labeled out of the noise.
I wanted to be able to drive it. So there’s a studio: build your own traces by
piping operators onto x, splitting nodes into branches, or loading a verified
construction and tweaking it. When your hand-built tree happens to equal a known
function, the scope says so.
Open the One Operator studio →
(This post is a placeholder — more on the motivation, and the strange beauty of a single operator, to come.)