enumeratio

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Manipulate ​

A generic, Wolfram-style Manipulate, rendered by <notatio-manipulate>. It shows a slider (or setter) per parameter and re-binds those parameters into any slotted content: every descendant attribute that is a notatio expression carrying a named wildcard (_a) is a template, re-evaluated live as the controls move. The same wrapper drives a plot, a glyph, several elements at once, or plain markup.

params uses Wolfram's control tuples — {a, min, max}, {a, min, max, step}, { {a, init}, min, max }, and a discrete {k, {1, 2, 3}}; separate several with ; or ,. A slot is a named wildcard filled from the matching control: _a takes the value of a, and the slot body can be any notatio expression over them (_n, _n * 20, _A / 2). Every slider carries a play button (▶) that animates it on a loop.

Authoring note

_a wildcards are plain text — no framework escaping needed. The wrapper is still written with v-pre only so VitePress leaves the literal { … } control tuples in params alone. In a plain HTML host (or a REPL) it is just <notatio-manipulate params="…">…</notatio-manipulate>. Plots and surfaces also accept a params attribute directly — a shorthand for the common single-child case.

Controls sit above the content by default, as in Wolfram's own Manipulate — a panel underneath a tall plot can fall off the bottom of the screen. controls="below" flips that. fps adds a frame-rate readout, shown only while a slider is playing.

Dragging a slider applies immediately. Play is what interpolates: it advances continuously, covering one step per tick but moving through the values in between, so a swept parameter reads as motion rather than as a sequence of jumps. A whole-number step — an order, a count — stays on its grid regardless, since half of an integer order is not a thing you want to plot.

Drive a curve ​

A frequency knob

The slider fills the wildcard _a in the plot's value and re-samples. Press ▶ to sweep it.

source
<notatio-manipulate params="{a, 1, 5}">
  <notatio-plot value="Sin(_a * x)" domain="-6.283,6.283" />
</notatio-manipulate>

Amplitude · frequency · phase

source
<notatio-manipulate params="{ {A, 1}, 0, 2}; { {w, 2}, 0.5, 6}; {p, 0, 6.283}">
  <notatio-plot value="_A * Sin(_w * x + _p)" domain="-6.283,6.283" plot-range="-2,2" />
</notatio-manipulate>

Drive a glyph ​

Grow a subset

Here _n is the ground-set size of a subset glyph — the same control machinery, a different representation.

source
<notatio-manipulate params="{ {n, 4}, 1, 8, 1}">
  <notatio-figure kind="subset" value="[1,3]" n="_n" />
</notatio-manipulate>

One control, several views ​

A curve and its harmonic index

One slider feeds two children at once — the plot's frequency and a glyph marking k in {1..6}.

source
<notatio-manipulate params="{ {k, 3}, 1, 6, 1}">
  <notatio-plot value="Sin(_k * x)" domain="-6.283,6.283" grid />
  <notatio-figure kind="subset" value="[_k]" n="6" />
</notatio-manipulate>

Animate ​

A travelling wave (press ▶)

source
<notatio-manipulate params="{t, 0, 6.283}">
  <notatio-plot value="Sin(x - _t)" domain="-6.283,6.283" />
</notatio-manipulate>

loop on the wrapper says what playback does at the ends — cycle (the default, Manipulate's own), reflect or none — and holding ▶ (or right-clicking it) opens a panel for that and for the speed, per slider. The same attribute and panel serve a plot's own params sliders and a worksheet's bindings.

Drive a surface ​

Sweep a surface frequency

source
<notatio-manipulate params="{ {k, 1}, 0.5, 3}">
  <notatio-plot-3d value="Sin(_k * x) * Cos(_k * y)" x-domain="-3.14,3.14" y-domain="-3.14,3.14" />
</notatio-manipulate>

A discrete choice ​

A setter over a list

source
<notatio-manipulate params="{k, {1, 2, 3, 5}}">
  <notatio-plot value="Sin(_k * x)" domain="-6.283,6.283" grid />
</notatio-manipulate>

A sentence for a panel ​

Wolfram's Manipulate puts the controls in a strip, and the reader has to hold in their head which slider goes with which term. prose replaces the strip with a sentence: the same params declaration, but each parameter appears where the prose mentions it, as a knob you drag, and any other expression in braces is a readout that follows. $…$ typesets. Every knob has the full Tangle gesture set — gears, keyboard, typing, and Space to play.

A control paragraph

Drag the 3 and the 1.0; press ▶ (or focus a knob and hit Space) to sweep. The readouts are ordinary <notatio-dynamic> templates and the plot is an ordinary Manipulate target — nothing in the sentence knows the plot exists.

source
<notatio-manipulate params="{ {k, 3}, 1, 8, 1}; { {a, 1}, 0.2, 2, 0.1}" prose="The curve $a\sin(kx)$ with frequency {k} and amplitude {a | play} crosses zero {2 * _k + 1} times on $[-\pi, \pi]$ and reaches {N(_a) | digits=2} at its peaks.">
  <notatio-plot value="_a * Sin(_k * x)" domain="-3.1416,3.1416" grid />
</notatio-manipulate>

A hole's options ride after a bar: {k | axis=y} drags vertically, {k | play} shows the play button, {k | autoplay} sweeps while on screen, {k | loop=reflect rate=2} sets how and how fast, {expr | digits=3} rounds a readout. The range, step and starting value stay in params, where Wolfram keeps them.

Roadmap ​

  • More control kinds (checkbox, 2-D locator, colour), matching Manipulate.
  • A Manipulate entry in the Symbol reference, with the Wolfram control-spec grammar alongside the live wrapper.