Conformal Map Visualizer

f (z) =
Parameters
a = b =
Preset
View

About

  • Draws the image of the unit disk (or exterior) under a complex map f. A polar grid of circles and radial rays is transported through f into the range.
  • Cell fills and grid lines are both colored by the argument of f′(z), making it easy to see how f rotates and stretches infinitesimal shapes. Where f′(z) = 0 (critical points), colors become singular.
  • The red point c and blue point d are complex parameters that can be dragged to update the map in real time.

Controls

  • Type a function in the f(z) field and press Enter.
  • Drag c (red) or d (blue) to update complex parameters live.
  • Set a, b (real parameters) and press Apply.
  • Drag the yellow grid slider to change grid density.

Predefined objects

  • Constants: e, pi, i.
  • Parameters: a, b (real); c, d (complex, draggable).
  • abs, sqrt, exp, log, sin, cos, tan, arcsin, arccos, arctan, re, im, conjugate.

Contact me at andrew@graven.com with any comments, suggestions, or feature requests.