Phase Portrait Lab

Phase Portrait Labcomplex functions, mapped and colored

Definitions

Saved setups live in this browser only — they are never published, and never travel in a shared link.

The mathematics of a scene: every row, in the words you typed, and which one is drawn. Plain text, so it pastes into a document, an email or a handout and can be typed back in by hand — and this page will still read it after the page has changed. The link carries more (the view, the colors, the masks) but only this version of the page can read that.

Everything in the scene. Type in a row to make anything: a function f(z) = …, a point z₁ = …, an equation x² + y² = 1. + new adds a row, and its caret starts from a kind.

A row’s icon shows or hides it; its ▸ opens its settings, and the ? there says how that kind of row is written.

Coloring

Modulus contours (|f| ×2 each ring) Phase contours (12 sectors)

show: grid axes labels

White background (for screenshots printed on paper)

Lines and labels (kept in this browser only)

widthopacitycolor Axes Grid Modulus Phase

Labelspx bold

Numberssignificant digits (kept in this browser only)

Objects text100%

Settings text100%

Reference wheel

w plane

Objects

Snap points to grid (handles only) Disc annulus & sector too — drag its handles

disc 1 of 1

outer r1

inner r0

start θ0π

end θ2π

circles3

spokes8

lives in

Grid drag its handles

grid 1 of 1

size×

lines ∥13

lines ⊥13

cell×□

right angle lock cell

pixels

lives in

trails while dragging

Draw sketch on either plane

Image…

Images can also be dropped onto either plane, or pasted (⌘V / Ctrl+V).

Hue is the phase φ(f(z)); arg values use the branch (−π, π].
Complex Analysis · Block 1 · Proof School

Nothing here yet — examples appear as they debut in class.

Draw these terms at the probe

terms6

tip‑to‑tail1

Phase Portrait Lab

z plane

z sphere

drag to orbit · scroll to zoom

r = 1

sphere center R = 0.500

|f| over z

drag to orbit · scroll to zoom

1.00×

w plane

w sphere

drag to orbit · scroll to zoom

sphere center R = 0.500

|f| over w

drag to orbit · scroll to zoom

1.00×