Conformal Map Visualizer

f(z) = 

Parameters
a =   b =   
View
Presets


About

  • This tool draws the image of the unit disk (or its exterior) under a complex map f. A polar grid of circles and radial rays is drawn in the domain and transported through f into the range.
  • Grid lines are 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 on the canvas to update the map in real time.

Controls

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