<notatio-complex-plot>
<notatio-complex-plot value="PolyLog(2, z)"> -- domain-colouring of a complex-valued expression over the complex plane, one GPU invocation per pixel: hue is the argument, brightness a compressed log-magnitude, poles white and zeros black.
Any expression the complex emitter can lower works, so this replaces a hand-written shader per function. Under <notatio-manipulate> every constant becomes an axis:
``html <notatio-manipulate params="{s, 0.5, 6, 0.05}"> <notatio-complex-plot value="PolyLog(_s, z)" mask="1" /> </notatio-manipulate> ``
A slider moves a literal, not the expression's shape, so the compiled pipeline is reused and the frame costs one small uniform upload -- which is what lets Manipulate interpolate between slider steps and still hold frame.
mask dims everything outside that radius, for a series whose disk of convergence is part of the story (the polylog's |z| < 1). Drag to pan, scroll to zoom.
Framing is manipulable too: extent="_e" takes a wildcard directly, and center accepts the notatio list form [_c, 0] as well as a bare re,im.
Attributes
| Attribute | Type | Default | Notes |
|---|---|---|---|
value | string | "" | The complex-valued expression to colour, in notatio. |
var | string | "z" | The complex variable; defaults to z. |
center | string | "0,0" | Centre of the view in the complex plane, as re,im. Dragging pans it. |
extent | number | 2.4 | Half-width of the view. Scrolling zooms it. |
mask | number | 0 | Dim everything outside this radius; 0 masks nothing. |
height | number | 460 | Canvas height in pixels. |
fps | boolean | false | Show a frame-rate readout. |