Explore

Things to turn over in your hands. Each page takes one function — or one family of functions — and wires its every constant to a dial, so the question is not "what does this do" but "what happens when I move this".

The guides explain; these pages let you poke. Where a claim here is better made in prose, it links back.

• The two-argument zeta — the Hurwitz zeta and its generalized cousin, by Euler–Maclaurin: a surface, the closed forms, and where the two conventions part ways.
  • ζ on the GPU: a phase portrait — the whole kernel compiled to a WebGPU shader, colouring the complex -plane in real time.
• The Lerch transcendent — , the one function above the zeta/polylog/eta family, with a GPU domain-colouring of its disk of convergence.
• The polylog and the polygamma — and , both of them the Lerch series or the Hurwitz kernel in disguise, and two GPU portraits that look nothing alike.
• Fractals — the Mandelbrot and Julia sets of , coloured by the -th iterate itself rather than an escape count, with and on dials.

How these are built

Every dial on these pages is a <notatio-manipulate> wrapped around a plotting component, with the swept constants written as named wildcards (_s, _a) in the expression itself. Nothing here is bespoke: the same components are documented in the component reference and exercised one at a time in the playground. If a page here suggests a rig you want, you can build it.