enumeratio

Appearance

Vector & Stream Plot ​

Planar vector fields, rendered by <notatio-vector-plot>. The two components u(x, y) and v(x, y) are given in notatio (or both at once via field), each compiled to a native function and sampled on an n×n grid of cell centres.

Two modes share the element:

  • type="vector" (the default) — Wolfram's VectorPlot: one arrow per sample, its length and colour scaling with |F|. Arrows are capped at 90% of a cell, so neighbours never collide.
  • type="stream" — Wolfram's StreamPlot: streamlines traced from the same grid by fixed-step RK4 on the normalised field, so the step is arc length and a fast region doesn't outrun a slow one. Integration runs both ways from each seed and stops at the frame, at a singularity, or at a stagnation point. No random seeding — the same field always draws the same picture.

Vector fields ​

Rigid rotation

F = (−y, x): the arrows circulate, and their length grows with the distance from the origin.

source
<notatio-vector-plot u="-y" v="x" xrange="-2,2" yrange="-2,2" />

A saddle

field gives both components at once — a comma-separated pair, optionally wrapped in \{…\}.

source
<notatio-vector-plot field="x, -y" xrange="-2,2" yrange="-2,2" label="(x, −y)" />

A trigonometric field

n sets the arrow grid's resolution.

source
<notatio-vector-plot u="Sin(y)" v="Cos(x)" xrange="-3.14,3.14" yrange="-3.14,3.14" n="16" />

Streamlines ​

Rotation, as streamlines

The circular orbits of F = (−y, x). Each line carries one mid-line arrowhead showing the flow direction.

source
<notatio-vector-plot type="stream" u="-y" v="x" xrange="-2,2" yrange="-2,2" />

A dipole-like flow

steps caps the RK4 steps taken in each direction from a seed — longer lines at the cost of more integration.

source
<notatio-vector-plot type="stream" u="x^2 - y^2" v="2 * x * y" xrange="-2,2" yrange="-2,2" n="11" steps="80" />

Shear flow

source
<notatio-vector-plot type="stream" u="y" v="Sin(x)" xrange="-3.14,3.14" yrange="-2,2" n="10" x-label="x" y-label="y" />

Roadmap ​

  • Per-streamline arrowheads at a fixed arc-length spacing, not just mid-line.
  • Seed thinning, so streamlines don't crowd where the field converges.
  • Manipulate-style parameter sliders (params), matching Plot/Plot3D.